1 Introduction↩︎

It is well known that a linear \([n,k,d]_q\) code \(C\) corresponds to a multiset of \(n\) points in the projective space \(\mathrm{PG}(k-1,q)\) such that each hyperplane contains at most \(n-d\) elements. Therefore, instead of asking for linear codes with a large minimum Hamming distance \(d\) we can also ask for large multisets of points where not too many elements are contained in a hyperplane. If we replace points by \((h-1)\)-spaces the coding theoretic equivalent is given by additive codes over \(\mathbb{F}_{q^h}\), which are linear over \(\mathbb{F}_q\). Considering multisets of points such that at most \(s\) are contained in any subspace of codimension \(f\) corresponds to linear codes with a large \(f\)th generalized Hamming weight. Here we want to consider the maximum number \(n_q(r,h,f;s)\) of \((h-1)\)-subspaces in \(\mathrm{PG}(r-1,q)\) with the property each subspace of codimension \(f\) contains at most \(s\) elements. In coding theory terms we are dealing with additive codes that have a large \(f\)th generalized Hamming weight. The special cases where \(h\) or \(f\) equals \(1\) have been extensively studied. Outside of this regime not much seems to be known. By taking the complement we can relate our problem to a dual problem: what is the minimum number \(b_q(r,h,f;s)\) of \((h-1)\)-spaces in \(\mathrm{PG}(r-1,q)\) where each subspace of codimension \(f\) contains at least \(s\) elements? If \(s=1\) one also speaks of blocking sets of \((h-1)\)-spaces w.r.t.\((r-f-1)\)-spaces. The case \(h=f=1\) is a classical problem, and we e.g.have \(b_q(3,1,1;1)=q+1\) attained by all points on a line in \(\mathrm{PG}(2,q)\), which is also called a trivial blocking set. For non-trivial blocking sets, which are those not containing a full line in its support, the minimum size rises to \(3(p+1)/2\) for odd primes \(p\) [1]. For \(h=2\) and \(r-f=3\) we refer to e.g.[2]–[4]. If \(s>1\) one speaks of multiple blocking sets, see e.g.[5]. In [6] the authors speak of an \(s\)-fold \(f\)-blocking set of \(\mathrm{PG}(r-1,q)\) for the special case \(h=1\). In this paper, we use the following definition.

Whenever the parameters are clear from the context, we just speak of generalized blocking sets.

The remaining part of this paper is structured as follows. In Section 2 we introduce the necessary preliminaries. The relation between the geometric objects and coding theory is outlined in Section 3. In Section 4 we summarize our knowledge on the asymptotic behavior of \(n_q(r,h,f;s)\). General constructions are studied in Section 5. In Section 6 we investigate the generalized blocking sets and their minimum possible size \(b_q(r,h,f;s)\). In Section 7 we study the maximum number of lines in \(\mathrm{PG}(4,q)\) such that each plane contains at most \(s\) lines, and we fully determine \(b_2(5,2,2;s)\) as a function of \(s\). We close with a conclusion and a few open problems in Section 8. Sporadic blocking sets, found by integer linear programming searches, are listed in Appendix 9.

2 Preliminaries↩︎

The set of all subspaces of \(\mathbb{F}_q^r\), ordered by the incidence relation \(\subseteq\), is called the \((r-1)\)-dimensional projective geometry over \(\mathbb{F}_q\) and denoted by \(\mathrm{PG}(r-1,q)\). Here we use the projective dimension, so that an \((i-1)\)-space in \(\mathrm{PG}(r-1,q)\) is an \(i\)-dimensional space in the vector space setting \(\mathbb{F}_q^r\). We will call \(0\)-, \(1\)-, \(2\)-, \(3\)-, and \((r-2)\)-spaces points, lines, planes, solids, and hyperplanes, respectively. For two subspaces \(S\) and \(S'\) we write \(S\subseteq S'\) if \(S\) is contained in \(S'\). Moreover, we say that \(S\) and \(S'\) are incident if and only if \(S\subseteq S'\) or \(S\supseteq S'\). Let \([i]_q:=\tfrac{q^i-1}{q-1}\) denote the number of points of an arbitrary \((i-1)\)-space in \(\mathrm{PG}(r-1,q)\) where \(r\ge i\). By convention we set \([0]_q:=0\). More generally, by \(\genfrac{[}{]}{0pt}{}{r}{i}_{q}:=\tfrac{\prod_{j=0}^{i-1} q^{r-j}-1}{\prod_{j=0}^{i-1} q^{i-j}-1}=\tfrac{\prod_{j=0}^{i-1} [r-j]_q}{\prod_{j=0}^{i-1} [i-j]_q}\) we denote the number of \((i-1)\)-spaces in \(\mathrm{PG}(r-1,q)\). Duality implies \(\genfrac{[}{]}{0pt}{}{r}{i}_{q}=\genfrac{[}{]}{0pt}{}{r}{r-i}_{q}\). It is known that the number of \(j\)-spaces disjoint from a fixed \(m\)-space in \(\mathrm{PG}(n, q)\) equals \(q^{(m+1)(j+1)}\genfrac{[}{]}{0pt}{}{n-m}{j+1}_{q}\), see [7].

We can represent an \((i-1)\)-space in \(\mathrm{PG}(r-1,q)\) by an \(i\times r\) generator matrix over \(\mathbb{F}_q\). A multiset of points \(\mathcal{M}\) in \(\mathrm{PG}(r-1,q)\) is a mapping from the set of points to \(\mathbb{N}\). For a given point \(P\) we call \(\mathcal{M}(P)\) its multiplicity. We say that \(\mathcal{M}\) is spanning if the points with positive multiplicity span the entire ambient space. The notion of the point multiplicities is extended additively to any subspace \(S\) via \(\mathcal{M}(S):=\sum_{P\in S} \mathcal{M}(P)\). The relation between multisets of points and linear codes is explained in detail in Section 3. For additive codes we need the following generalization, see e.g.[8].

A faithful projective \(1-(n,r,s)_q\) system \(\mathcal{S}\) is just a multiset of points with cardinality \(n\) in \(\mathrm{PG}(r-1,q)\) with the property that the maximum hyperplane multiplicity \(\mathcal{S}(H)\) equals \(s\). Unfaithful projective \(h-(n,r,s)_q\) systems also allow the containment of \((-1)\)-dimensional subspaces, which correspond to zero columns in the generator matrix of a corresponding linear code for \(h=1\), see Section 3.

Note that the elements of \(\mathcal{S}\) span the entire ambient space \(\mathrm{PG}(r-1, q)\) if and only if \(s<n\). If \(\mathcal{S}\) is a projective \(h-(n, r, s)_q\) system that is not faithful, then we can easily construct a faithful projective \(h-(n, r, \le s)_q\) system \(\mathcal{S}'\) by replacing each element \(S\in\mathcal{S}\) with dimension smaller than \(h-1\) by an arbitrary \((h-1)\)-space containing \(S\). The functions \(n_q(r,h;s)\) were e.g.studied in [9], and indirectly in any paper on additive codes with good parameters.

For our situation we need an even more general notion.

A projective \((h,1)-(n,r,s)_q\) system is just a projective \(h-(n,r,s)_q\) system, and a general projective \((h,f)-(n,r,s)_q\) system corresponds to an additive \([n,r/h,d_f]_q^h\) code \(C\) with \(s=n-d_f\). Here \(d_f\) denotes the minimum \(f\)th generalized Hamming weight of \(C\), see Section 3. The parameter \(\mu\) corresponds to the maximum column multiplicity of linear codes over \(\mathbb{F}_q\), if we identify linear dependent non-zero columns of a generator matrix.

Clearly we can convert any given projective \((h,f)-(n,r,s)_q\) system into a faithful projective \((h,f)-(n,r,\le s)_q\) system by replacing each element \(U\) by an arbitrary \((h-1)\)-space containing \(U\).

By \(\dim(U)\) we denote the projective dimension of a subspace \(U\) in \(\mathbb{F}_q^n\), which is one less than the algebraic dimension. With this, the subspace distance is given by \(d_S(U,V)=\left(\dim(U)+1\right)+\left(\dim(V)+1\right)-2(\dim(U\cap V)+1)=\dim(U)+\dim(V)-2\dim(U\cap V)\), which is an even number if \(\dim(U)=\dim(V)\).

By \(A_q(v,k;2\delta)\) we denote the maximum number of \((k-1)\)-spaces in \(\mathrm{PG}(v-1,q)\) with minimum subspace distance \(2\delta\). Here we have \(\dim(U\cap V)+1\le k-\delta\) and speak of constant-dimension codes. In the following we give an upper bound and one simple construction for constant-dimension codes. In order to keep the paper self-contained we give a brief proof and description. For more details we refer to the survey [10].

A rank metric code \(M\) is a subset of \(m\times n\) matrices over \(\mathbb{F}_q\) equipped with the rank distance \(d_r(M,M')=\operatorname{rk}(M-M')\). Assuming \(m\le n\), a Singleton-like upper bound is known and gives \(|M|\le q^{n(m-\delta+1)}\) for minimum rank distance \(\delta\) [11]. Codes attaining this bound are called maximum rank distance (MRD) codes. They exist for all parameters, even if one additionally assumes that the matrices form a linear space, i.e.assuming that the code is linearly closed. For a survey on MRD codes we refer to [12]. Given an MRD code \(M\) of \(m\times n\) matrices over \(\mathbb{F}_q\) with minimum rank distance \(\delta\), we obtain a lifted MRD (LMRD) code \(\mathcal{M}\) by prepending \(m\times m\) unit matrices. Interpreted as generator matrices of \((m-1)\)-spaces in \(\mathrm{PG}(n+m-1,q)\), \(\mathcal{M}\) is a set of \(q^{n(m-\delta+1)}\) \((m-1)\)-spaces in \(\mathrm{PG}(n+m-1,q)\) such that the dimension of the intersection of any two elements is at most \((m-\delta-1)\) and there exists a special \((n-1)\)-space \(S\) that is disjoint to all elements of \(\mathcal{M}\).

3 Relation to coding theory↩︎

A linear \([n,k]_q\) code \(C\) is a \(k\)-dimensional subspace of the vector space \(\mathbb{F}_q^n\). The elements of \(C\) are called codewords and the Hamming weight \(\operatorname{wt}(c)\) of a codeword \(c\in C\) is the number of non-zero entries. With this, the Hamming distance \(d\!\left(c_1,c_2\right)\) between two codewords is given by \(\operatorname{wt}\!\left(c_1-c_2\right)\). The minimum Hamming distance \(d(C)\) of a (linear) code is the minimum Hamming distance \(d\!\left(c_1,c_2\right)\) between two different codewords. We say that an \([n,k]_q\) code \(C\) is an \([n,k,d]_q\) code if its minimum Hamming distance \(d(C)\) equals \(d\). A linear code is called \(\Delta\)-divisible if the weights of all codewords are divisible by \(\Delta\). If the non-zero weights of a linear \([n,k]_q\) code are contained in \(\left\{w_1,\dots,w_l\right\}\) we also speak of an \(\left[n,k,\left\{w_1,\dots,w_l\right\}\right]_q\) code, and an \(l\)-weight code if all weights are attained. As a representation for a linear code we use a \(k\times n\) generator matrix over \(\mathbb{F}_q\). The dual code \(C^\perp\) of an \([n,k]_q\) code \(C\) is the \([n,n-k]_q\) code whose codewords are orthogonal to all codewords in \(C\). By \(d^\perp\) we denote the corresponding minimum Hamming distance. We say that \(C\) has full length if \(d^\perp\ge 2\), which is equivalent to the property that there is no zero-column in a given generator matrix for \(C\). It is well known that full length \([n,k]_q\) codes are in one-to-one correspondence to spanning multisets of cardinality \(n\) in \(\mathrm{PG}(k-1,q)\), see e.g.[13].³ The minimum Hamming distance \(d\) of a linear code corresponds to the geometric property that the maximum number of elements of the multiset of points that is contained in a hyperplane is given by \(n-d\). So, a large minimum Hamming distance corresponds to a small maximum number of points in hyperplanes. Alternatively, minimizing the possible length \(n\) of an \([n,k,d]_q\) is equivalent to maximizing the cardinality of a multiset of points in \(\mathrm{PG}(k-1,q)\) with at most \(s\) points in each hyperplane, where \(s=n-d\).

More generally, a block code \(C\) of length \(n\) over the alphabet \(\mathbb{F}_q\) is just a subset of \(\mathbb{F}_q^n\) (equipped with the Hamming metric). If \(C\) is linearly closed, i.e.if \(c,c'\in C\) and \(\alpha,\beta\in\mathbb{F}_q\) implies \(\alpha c+\beta c'\in C\), then we have a linear \([n,k]_q\) code, where \(k=\log_q |C|\) is called the dimension. An additive code is just a block code that is additively closed, i.e.\(c,c'\in C\) implies \(c+c'\in C\). Each additive code is linear over some subfield, see e.g.[14]. By an \([n,r/h,d]_q^h\) code we denote an additive code \(C\subseteq \mathbb{F}_{q^h}^n\) that is linear over \(\mathbb{F}_q\), has minimum Hamming distance \(d\) and cardinality \(q^r\). We call \(r/h\in\mathbb{Q}\) its dimension. We can represent an \([n,r/h,d]_q^h\) code as the \(\mathbb{F}_q\) row span of an \(r\times n\) generator matrix \(G\) over \(\mathbb{F}_{q^h}\). Choosing an \(\mathbb{F}_q\) basis of \(\mathbb{F}_{q^h}\) we can expand this generator matrix to a subfield generator matrix \(\widetilde{G}\in\mathbb{F}_q^{r\times nh}\). By \(\mathcal{X}_G(C)\) we define the multiset of the \(n\) subspaces spanned by the \(n\) blocks of \(h\) columns of \(\widetilde{G}\) in this way. Note that these subspaces give rise to projective systems.

The parameters of a linear \([n,k,d]_q\) code \(C\) are related by the so-called Griesmer bound [15], [16] \[\label{eq95griesmer95bound} n\ge \sum_{i=0}^{k-1} \left\lceil\frac{d}{q^i}\right\rceil=:g_q(k,d).\tag{1}\] From this one can derive the bound \[\begin{align} n&\ge& \left\lceil \frac{g_q\!\left(r,d\cdot q^{h-1}\right)}{[h]_q} \right\rceil = \left\lceil \frac{ \sum\limits_{i=0}^{r-1} \left\lceil d\cdot q^{h-1-i}\right\rceil}{[h]_q} \right\rceil\nonumber\\ &=&d+\left\lceil\frac{\sum\limits_{i=1}^{r-h} \left\lceil\frac{d}{q^i}\right\rceil}{[h]_q}\right\rceil = d+ \left\lceil \frac{g_q(r-h+1,d)-d }{[h]_q}\right\rceil \end{align}\] for the parameters of an additive \([n,r/h,d]_q^h\) code, see e.g.[8] or [9]. Using Theorem 1 this gives an upper bound for \(n_q(r,h,1;s)\), which we call the Griesmer upper bound. More precisely, we call the largest integer \(n\) that satisfies \([h]_q\cdot n\ge g_q\!\left(r,(n-s)\cdot q^{h-1}\right)\) the Griesmer upper bound for \(n_q(r,h;s)\), see e.g.[9].

The Hamming weight \(\operatorname{wt}(c)\) turns \(\mathbb{F}_q^n\) into a normed vector space. For \(c=\left(c_1,\dots,c_n\right)\in\mathbb{F}_q^n\) we call \[\operatorname{supp}(c):=\left\{1\le i\le n\,:\, c_i\neq 0\right\}\] the support of \(c\), so that \(\operatorname{wt}(c)=|\operatorname{supp}(c)|\). For some linear subspace \(C\) in \(\mathbb{F}_q^n\) let \[\operatorname{supp}(C):=\left\{1\le i\le n\,:\, \exists c=\left(c_1,\dots,c_n\right)\in C, c_i\neq 0\right\}\] be the support of \(C\) and \(\dim_{\mathbb{F}_q}(C)\) its (algebraic) \(\mathbb{F}_q\)-dimension. For two \(\mathbb{F}_q\) vector spaces \(C\), \(C'\) in \(\mathbb{F}_q^n\) we write \(C\subseteq C'\) if \(C\) is contained in \(C'\). With this, the \(f\)th generalized Hamming weight of a linear code \(C\) [17], [18], denoted as \(d_f(C)\), is the size of the smallest support of an \(f\)-dimensional subcode of \(C\): \[\label{eq:dflinear} d_f(C):= \min\!\left\{|\operatorname{supp}(C')|\,:\, C'\subseteq C, \dim_{\mathbb{F}_q}(C')=f\right\}.\tag{2}\] In particular, \(d_1(C)\) is the minimum Hamming distance of a linear code \(C\). The sequence \(\left(d_1(C),\dots,d_k(C)\right)\) is called the weight hierarchy of a linear \([n,k]_q\) code \(C\). Clearly, we have \(1\le d_1(C)\le \dots\le d_k(C)\le n\). The generalized Hamming weights can be used to describe the cryptographic performance of a linear code over the wire-tap channel of type II [19]. Moreover, it van also be used to determine the trellis complexity of the code [20]–[23]. The weight hierarchy of a linear code can be obtained from a quadratic form over a finite field [24]–[26]. Also the geometric reformulation of the generalized Hamming weights in terms of multisets of points is well known [27], [28]. Let \(\mathcal{M}\) be a multiset of points in \(\mathrm{PG}(k-1,q)\) and \(C\) its corresponding \([n,k]_q\) code. Then, we have \[\label{eq95gen95ham95geometry} n-d_f(C) =\max\left\{\mathcal{M}(U)\,:\, U\text{ subspace of codimension }f \right\}\tag{3}\] for all \(1\le f\le k\). In order to keep the paper self-contained we state a brief argument, c.f.[29]. Given a linear \([n,k,d]_q\) code \(C\), a codeword (a \(1\)-dimensional subcode) of \(C\) is obtained by left multiplication of a generator matrix \(G\) by a vector \(v\in\mathbb{F}_q^k\). Considering \(v\) as a point in \(\mathrm{PG}(k-1, q)\), the hyperplane \(v^\perp\) contains the point \(x\) if and only if \(\langle v,x\rangle=0\). Therefore, if we take the set of \(n\) points in \(\mathrm{PG}(k-1,q)\), corresponding to the columns of \(G\), we have that the codeword \(vG\) has weight \(w\) if and only if \(n-w\) of these points are contained in the hyperplane \(v^\perp\). More generally, for a \(j\)-dimensional subspace \(V\) of \(\mathbb{F}_q^n\) the codimension \(j\) subspace \(V^\perp\) contains \(n-w\) points if the subspace \(\left\{vG\,:\, v\in V\right\}\) has support size \(w\), which proves Equation (3 ). We can apply the same argument to the subfield generator matrix \(\widetilde{G}\) of an additive \([n,r/h,d]_q^h\) code \(C\) to conclude \[\label{eq95gen95ham95geometry95add} n-d_f(C) =\max\left\{\left|\left\{S\in\mathcal{X}_G(C)\,:\, S\le U\right\}\right|\,:\, U\text{ subspace of codim. }f \right\}\tag{4}\] for all \(1\le f\le k\). Hence, looking for good additive codes, corresponds to look for large projective systems.

Currently we do not know any Griesmer type bound for the \(f\)th generalized Griesmer weight of additive codes, which is tight for all sufficiently large minimum distances. This is an important open problem. For \(f>1\) and \(h>1\) we cannot reconstruct the number of \((h-1)\)-spaces in a codimension \(f\) space from the number of contained points and the total number of \((h-1)\)-spaces.

4 Asymptotic results↩︎

We first state a sum construction and an easy upper bound that can be asymptotically attained.

Considering the set of all \(n=\genfrac{[}{]}{0pt}{}{r}{h}_{q}\) \(h\)-spaces in \(\mathrm{PG}(r-1,q)\) we see that the upper bound in Lemma 3 is tight for \(s=\genfrac{[}{]}{0pt}{}{r-f}{h}_{q}\). Using \(\lambda\) copies of this construction yields \[\lim_{s\to\infty} n_q(r,h,f;s) \cdot \frac{\genfrac{[}{]}{0pt}{}{r-h}{f}_{q}}{\genfrac{[}{]}{0pt}{}{r}{f}_{q}\cdot s}=1.\] For \(f=1\) the Griesmer bound implies that the difference between \(n_q(r,h,1;s)\) and the corresponding Griesmer upper bound tends to zero if \(s\) tends to infinity, which is a much tighter statement.⁴ The same stronger result also holds for the cases where \(h=1\) and \(f\) is arbitrary. Of course it would be very interesting to have such a result in general. However, the relation to constant-dimension codes in Lemma 4 indicates that this might be a hard problem.

Instead of letting \(s\) tend to infinity we can also consider \(n_q(r,h,f;s)\) as a sequence in the field size \(q\).

The special case \(\delta=h\) corresponds to partial spreads where many bounds are known, see e.g.[31]. For general parameters the following construction using (L)MRD codes is well known.

As an example, for \(r=6\), \(h=3\), and \(\delta=2\) we obtain a set of \(q^6\) planes in \(\mathrm{PG}(5,q)\) with the property each solid contains at most one plane (and each \(4\)-space contains at most \(q^3\) planes). Via Lemma 4 we can replace the used LMRD codes by any other constant-dimension code with the same minimum subspace distance, see e.g.[10] for a survey on some constructions from the literature. For the aforementioned parameters we remark that this construction is not optimal, since there is a construction known with \(q^6+2q^2+q+1\) planes, see [32].

For the special cases where either \(r=2h\) or \(s=1\) the construction with the LMRD codes is asymptotically tight if \(q\) tends to infinity.

To prove this, we use the so-called \(q\)-Pochhammer symbol \[(a;q)_n=\prod_{i=0}^{n-1} \left(1-aq^i\right).\] In particular, we will use that \[\label{ie95qbin} 1\le q^{-b(a-b)}\cdot \genfrac{[}{]}{0pt}{}{a}{b}_{q} \le \frac{1}{(1/q;1/q)_b},\tag{5}\] see e.g.[33].

As in the proof of Proposition 7, Lemmas 1 and 4, together with Inequality (5 ) yield the upper bound, while Proposition 6 provides a matching lower bound.

We remark that Lemma 1 is known as the anticode bound in the context of subspace codes and that tighter bounds are known, see e.g.[10].

5 General constructions↩︎

In this section we want to study known constructions for linear codes from the literature and generalize them to our context.

In coding theory it is well known that the problem of determining the minimum possible length of an \([n,k,d]_q\) code as a function of \(d\) is a finite problem for given parameters \(k\) and \(q\). More precisely, if the minimum distance \(d\) is sufficiently large, then the Griesmer bound can always be attained with equality. A corresponding construction was given by Solomon and Stiffler [16]. In geometric terms this means that the determination of the function \(n_q(r,1,1;\cdot)\) in terms of \(s\) is a finite, but still rather hard, problem for each given pair of parameters \(r\) and \(q\). In [9] this result was generalized to additive codes, i.e.also applies to \(n_q(r,h,1;\cdot)\) for arbitrary \(h\). In order to describe the Solomon–Stiffler construction and its generalization, we have to introduce further notation. For each subspace \(S\) in \(\mathrm{PG}(r-1,q)\) we denote its characteristic function by \(\chi_S\), i.e.we have, for a point \(P\in PG(r-1,q)\) that \(\chi_S(P)=1\) if \(P\in S\) and \(\chi_S(P)=0\) otherwise.

To ease the notation and to avoid technical difficulties, we choose a chain of subspaces \(S_1\subseteq S_2\subseteq\dots\subseteq S_r\) in \(\mathrm{PG}(r-1,q)\), where \(S_i\) has projective dimension \((i-1)\).

For example, we trivially have that \(S_3\) is \(3\)-partitionable over \(\mathbb{F}_q\). The existence of plane spreads in \(\mathrm{PG}(5,q)\) implies that \(S_6\) is \(3\)-partitionable over \(\mathbb{F}_q\). Since \([7]_q\) is not divisible by \([3]_q\), we have that \(S_7\) is not \(3\)-partitionable over \(\mathbb{F}_q\), while \((q^2 + q + 1)\cdot S_7\) is \(3\)-partitionable. For the details on the underlying constructions we refer to [9].

Using a specific parameterization of the minimum distance \(d\) the Griesmer bound in Inequality (1 ) can be written more explicitly as follows. Let \(k\) and \(d\) be positive integers. Write \(d\) as \[\label{eq95griesmer95representation95min95dist} d=\sigma q^{k-1}-\sum_{i=1}^{k-1}\varepsilon_iq^{i-1},\tag{6}\] where \(\sigma\in\mathbb{N}_{>0}\), and the \(0\le\varepsilon_i<q\) are integers for all \(1\le i\le k-1\). Then, Inequality (1 ) is satisfied with equality if and only if \[\label{eq95griesmer95representation95length} n=\sigma[k]_q-\sum_{i=1}^{k-1}\varepsilon_i[i]_q,\tag{7}\] which is equivalent to \[\label{eq95griesmer95representation95species} n-d=\sigma[k-1]_q-\sum_{i=1}^{k-1}\varepsilon_i[i-1]_q.\tag{8}\]

Given arbitrary \(\varepsilon_1,\dots,\varepsilon_{k-1}\in\mathbb{Z}\), we have that \(\mathcal{M}=\sigma \chi_{S_k}-\sum_{i=1}^{k-1}\varepsilon_i\chi_{S_i}\) is a multiset of points in \(\mathrm{PG}(k-1,q)\), which is a projective \(1-(n,k,s)_q\) system for all sufficiently large \(\sigma\in\mathbb{N}\). Here \(n=\sigma [k]_q-\sum_{i=1}^{k-1}\varepsilon_i[i]_q\) and \(s=\sigma [k-1]_q-\sum_{i=1}^{k-1}\varepsilon_i[i-1]_q\), see e.g.[9]. While \(\sigma S_k-\sum_{i=1}^{k-1}\varepsilon_i S_i\) is obviously \(1\)-partitionable over \(\mathbb{F}_q\) if \(\sigma\) is sufficiently large, there are further conditions for being \(h\)-partitionable when \(h>1\) as well as more sophisticated constructions for the partition, see [9].

Recall that a multiset \(\mathcal{M}\) of \((h-1)\)-spaces in \(\mathrm{PG}(r-1,q)\) is an \(s\)-fold blocking set w.r.t.\((v-1)\) spaces if every \((v-1)\)-space in \(\mathrm{PG}(r-1, q)\) contains at least \(s\) elements from \(\mathcal{M}\). Note that the smallest size of an \(s\)-fold blocking set w.r.t. \((v-1)\)-spaces in \(\mathrm{PG}(r-1,q)\) is denoted by \(b_q(r,h,r-v;s)\). Whenever the parameters are clear from the context, we just speak of generalized blocking sets.

A first attempt to generalize the Solomon–Stiffler construction is given by the following lemma.

Choosing \(\sigma=\varepsilon_4=1\) we e.g.obtain \(n_2(5,2,2;6)\ge 120\). Similarly, \(\sigma=\varepsilon_4=2\) yields \(n_2(5,2,2;12)\ge 240\).

The essential idea in the proof of Lemma 5 is the blocking property of subspaces, so that we state the following alternative.

In Section 6 we will consider blocking sets that have a smaller cardinality than the one consisting of all \((h-1)\)-spaces in a fixed subspace.

A simple but very effective variant of Lemma 6 is given by the removal of a single blocking set.

6 Blocking sets↩︎

In Section 1 we have introduced the notion \(b_q(r,h,f;s)\) for the minimum size of an \(s\)-fold blocking set of \((h-1)\)-spaces with respect to subspaces of codimension \(f\). Recall that this is the minimum number of \((h-1)\)-spaces in \(\mathrm{PG}(r-1,q)\) such that each subspace of codimension \(f\) contains at least \(s\) members. If we additionally assume that the maximum multiplicity of an \((h-1)\)-space is \(m\), then we use the notation \(b_q(r,h,f;s,m)\) for the minimum possible cardinality. So, we obviously have \(b_q(r,h,f;s,m)\ge b_q(r,h,f;s,m')\) and \(b_q(r,h,f;s,m)\ge b_q(r,h,f;s)\) for all \(m,m'\in\mathbb{N}\) with \(m\le m'\). We note that allowing subspaces of projective dimension smaller than \(h-1\) would not decrease those numbers. A straightforward counting argument gives a first lower bound.

A well-known construction is to use all \((h-1)\)-spaces contained in a fixed \((h+f-1)\)-space. Furthermore, note that the union of two blocking sets again gives a blocking set. Using this, we get the following proposition and lemma.

From Proposition 12 we can e.g.conclude \(b_q(5,2,2;1)\le \genfrac{[}{]}{0pt}{}{4}{2}_{q}=q^4+q^3+2q^2+q+1\). Next we describe an improved construction from [2]. For a given integer \(l\ge 3\) consider \(\mathrm{PG}(2l-2,q)\) and an arbitrary point \(P\). With this, let \(\mathcal{S}\) be a set of \(\frac{q^{2l-2}-1}{q^2-1}\) planes through \(P\) that form a geometric line spread in the quotient geometry through \(P\). Fix an \(l\)-space \(U\) through \(P\). Let \(\mathcal{B}\) consist of the \(\frac{q^l-1}{q-1}\) lines in \(U\) through \(P\) together with the \(q^2\frac{q^{2l-2}-1}{q^2-1}\) lines that lie in a plane of \(\mathcal{S}\) but do not contain \(P\). Then every \((l-1)\)-space in \(\mathrm{PG}(2l-2,q)\) contains at least one line from \(\mathcal{B}\).

This construction is shown to be optimal in the theorem below.

We remark that in [2] sets of lines were considered. However, the statement remains obviously true for multisets of lines. For \(l=3\) we obtain \(b_q(5,2,2;1)= q^4+2q^2+q+1\), i.e.the subspace construction is improved by \(q^3\) lines.

6.1 The minimum number of lines in \(\mathrm{PG}(4,q)\) such that every plane contains at least \(s\) elements↩︎

In this subsection we want to focus on the values \(b_q(5,2,2;s)\). From Theorem 3, Proposition 12, and Lemma 9 we directly conclude:

In the following we present some constructions that are better for specific choices for \(s\) and we look into lower bounds improving upon Lemma 8.

For \(q=2\) the corresponding blocking set has size \(52\), which is indeed the minimum size for a double blocking set as verified by a small ILP computation, see Lemma 15. In Lemma 19 we give a lower bound, which shows that \(|B|\geq q^5+q^3+q^2+q\), so that Lemma 11 can be improved by at most \(q^3-q\).

For \(q=2\) this gives a \(3\)-fold blocking set of cardinality \(75\). By a sequence of ILP computations, see Lemma 16, we can verify that this is the minimum possible cardinality (even for multisets of lines).

For \(q=2\) this gives a \(4\)-fold blocking set of cardinality \(92\), whose minimality can be concluded from Lemma 19, see Theorem 4. However, there are lines that are taken four times. In Appendix 9 we list examples showing \(b_2(5,2,2;4,1)\le 102\) and \(b_2(5,2,2;4,2)\le 98\). The best known and indeed optimal construction for \(b_2(5,2,2;5)\) is given by \(b_2(5,2,2;5)\le b_2(5,2,2;1)+b_2(5,2,2;4)=27+92=119\), see Lemma 9. Again, this construction comes with a large maximum line multiplicity. Moreover, using ILP, we found examples to prove \(b_2(5,2,2;5,1)\le 123\), \(b_2(5,2,2;5,3)\le 121\), and \(b_2(5,2,2;5,4)\le 120\), see Appendix 9.

For \(q=2\) Lemma 14 gives a \(6\)-fold blocking set of cardinality \(138\), whose optimality is implied by Lemma 19, see Theorem 5. However, there exists a line that is taken six times, so that we give examples showing \(b_2(5,2,2;6,1)\le 146\), \(b_2(5,2,2;6,2)\le 142\), \(b_2(5,2,2;6,3)\le 142\), and \(b_2(5,2,2;6,5)\le 141\) in Appendix 9.

In Table ¿tbl:table95b952955952952? we have summarized the upper bounds for \(b_2(5,2,2;s)\) based on the constructions described so far, where \(1\le s\le 7\). For future reference we have added the currently best known upper bound for \(b_2(5,2,2;s,1)\) in the last column. Either the mentioned construction in the unrestricted cases automatically satisfies a maximum line multiplicity of one or the example was found by ILP computations. In the remaining part of this subsection we will present matching lower bounds. The lower bounds for \(s\in\{2,3,5\}\) were obtained by tailored ILP computations, see Lemma 15, Lemma 16, and Lemma 18, using the ILOG CPLEX solver.

We note that Lemma 23 is a complementary bound.

Since the construction in the proof of Lemma 13 gives the unique \(4\)-fold blocking set of \(92\) lines in \(\mathrm{PG}(4,2)\) w.r.t. planes, see Lemma 17, there is a unique example attaining \(b_2(5,2,2;4+7t)\) for all \(t\in \mathbb{N}\).

In Table ¿tbl:table95b953955952952? we fix \(q=3\) and summarize our knowledge on \(b_3(5,2,2;s)\) for \(1\le s\le 13\).

6.2 Generalizations to other parameters↩︎

The constructions from Lemma 13 and Lemma 14 can be described from a more general point of view. In \(\mathrm{PG}(r-1,q)\) let \(S_1,\dots,S_{r-1}\) be a chain of subspaces with \(\dim\!\left(S_i\right)=i-1\) for \(1\le i\le r-1\). The set of \((h-1)\)-spaces is partitioned into classes \(\mathcal{H}_1,\dots,\mathcal{H}_u\) according to the intersection dimensions with those \(S_i\). The set of subspaces of codimension \(f\) is partitioned into classes \(\mathcal{F}_1,\dots,\mathcal{F}_v\) according to the intersection dimensions with the \(S_i\). By \(\beta_{i,j}\) we denote the number of elements from \(\mathcal{H}_i\) that are contained in an arbitrary element \(\pi\in\mathcal{F}_j\). As blocking set we choose \(\mathcal{B}=\sum_{i=1}^u \alpha_i\mathcal{H}_i\), where \(\alpha_i\in\mathbb{N}\) for \(1\le i\le u\). Given this framework, we obtain a simple optimization problem: choose \(\alpha_i\in \mathbb{N}\) minimizing \(\sum_{i=1}^u \alpha_i\cdot \left|\mathcal{H}_i\right|\) such that \(\sum_{i}\alpha_i\beta_{i,j}\ge s\) for all \(1\le j\le v\). Of course also the easy construction from Proposition 12 can be described in this way.

We can generalize Lemma 19 as follows.

It seems tempting to generalize Theorem 4 (or Theorem 5). However, there are some issues that we cannot resolve. Motivated by Lemma 13 we state the following generalized construction:

So, we especially have \(b_q\!\left(6,2,3;q^2\right)\le q^8 + q^6+q^5+2q^4+q^3+q^2\). Applying Lemma 21 for these parameters with \(\mathcal{B}(L)=0\) gives \(b_q\!\left(6,2,3;q^2\right)\ge q^8 + q^6+q^5+q^4+q^3+q^2\), i.e.there remains a gap of \(q^4\). For \(q=2\) those bounds give \(380\le b_2(6,2,3;4)\le 396\). Solving our standard ILP model with the additional constraint \(x_L=0\), i.e.\(\mathcal{B}(L)=0\), gives \(b_2(6,2,3;4)=396\), so that Lemma 22 is optimal for \((r,q)=(5,2)\). We remark that the corresponding LP relaxation yields the lower bound \(b_2(6,2,3;4)\ge 380\) only, and hence, the bound in Lemma 21 is optimal for these parameters if we only rely on counting arguments and the extra information \(\mathcal{B}(L)=0\). Using \(\mathcal{B}(L)=0\) and \(\mathcal{B}(L')=0\) for two disjoint lines the corresponding LP relaxation gives \(b_2(6,2,3;4)\ge 385.3333\). For \(b_q\!\left(6,2,3;q^2+q\right)\) similar computations can be performed.

7 The maximum number of lines in \(\mathbf{\mathrm{PG}(4,q)}\) such that each plane contains at most \(\mathbf{s}\) lines↩︎

Here we want to determine bounds for \(n_q(5,2,2;s)\). Recall the correspondence, by duality, between \(n_q(5,2,2;s)\) and the generalized blocking sets. More precisely, if we have a configuration with maximum line multiplicity at most \(s\), then \(n_q(5,2,2;s) = s\cdot \genfrac{[}{]}{0pt}{}{5}{2}_{q}-b_q(5,2,2;s\cdot[3]_q-s,s)\).

From Lemma 5 we know that \(b_q(5,2,2;q^2+q) = (q^2+q)(q^4+q^2+q+1)\), which shows that here again, the last parameter \(m\) plays an important role.

We can easily formulate the problem of the determination of \(n_q(r,h,f;s)\) as an integer linear programming (ILP) problem. To this end let \(\mathcal{H}\) denote the set of all \((h-1)\)-spaces and \(\mathcal{F}\) denote the set of all \((r-f-1)\)-spaces in \(\mathrm{PG}(r-1,q)\). As variables we choose \(x_H\in\mathbb{N}\) for all \(H\in\mathcal{H}\) to model the multiplicities of the chosen \((h-1)\)-spaces. The condition that each subspace of codimension \(f\) contains at most \(s\) elements can be modeled as \(\sum_{H\in\mathcal{H}\,:\, H\subseteq F} x_H\le s\) for all \(F\in\mathcal{F}\). As target function we choose \(\sum_{H\in\mathcal{H}} x_H\), i.e.the number of selected \((h-1)\)-spaces. Typically this ILP can be solved directly for rather small values of \(r\), \(h\), \(f\), and \(q\) only. In order to obtain lower bounds we can e.g.prescribe some automorphisms. For upper bounds we can add tailored extra constraints or prescribe a few \((h-1)\)-spaces to reduce the symmetry of the formulation.

From Theorem 7 and Lemma 2 we have \(n_q(5,2,2;2)\ge 2\left(q^3+1\right)\in \Theta\!\left(q^3\right)\). From Lemma 3 we conclude \(n_q(5,2,2;2)\le 2\cdot \frac{\left(q^4+q^3+q^2+q+1\right)\cdot\left(q^2+1\right)}{q^2+q+1}\in\Theta\!\left(q^4\right)\), so that the question for the right order of magnitude, in terms of \(q\), arises. By ILP computations we found examples showing \(n_2(5,2,2;2)\ge 32\), \(n_3(5,2,2;2)\ge 97\), and \(n_5(5,2,2;2)\ge 493\). We remark that improved constructions for \(n_q(5,2,1;2)\) have been recently obtained in [36].

Actually, Lemma 7 and the construction of a blocking set in Lemma 12 imply the following lemma.

We have the summarized our information on \(n_2(5,2,2;s)\) in Table ¿tbl:table95bounds95n952955952952?.

We can easily generalize Lemma 23 to \(\mathrm{PG}(n,q)\). For an even more general version, formulated in terms of blocking sets, we refer to Lemma 21.

From Theorem 3, Lemma 11, Theorem 7, Lemma 19, and Proposition 12 we conclude \(b_3(5,2,2;1,1)=103\), \(b_3(5,2,2;3,1)\le 306\), \(b_3(5,2,2;12,1)= 1182\), and \(b_3(5,2,2;13,1)=1210\), respectively. For \(b_3(5,2,2;2,1)\le 206\), \(b_3(5,2,2;5,1)\le 550\), \(b_3(5,2,2;6,1)\le 648\), \(b_3(5,2,2;7,1)\le 745\), \(b_3(5,2,2;8,1)\le 844\), \(b_3(5,2,2;9,1)\le 935\), \(b_3(5,2,2;10,1)\le 1020\), and \(b_3(5,2,2;11,1)\le 1105\) we refer to Appendix 9. Using Lemma 7 we obtain the lower bounds for \(n_3(5,2,2;s)\) for \(1\le s\le 13\), as summarized in Table ¿tbl:table95bounds95n953955952952?.

8 Conclusion and open problems↩︎

We have introduced the maximum number \(n_q(r,h,f;s)\) of \((h-1)\)-spaces in \(\mathrm{PG}(r-1,q)\) such that each subspace of codimension \(f\) contains at most \(s\) elements. These numbers are complemented by the minimum number \(b_q(r,h,f;s)\) of \((h-1)\)-spaces in \(\mathrm{PG}(r-1,q)\) such that each subspace of codimension \(f\) contains at least \(s\) elements. Both notions are rather general. As an example, the case \((h,f)=(1,1)\) corresponds to linear codes with their geometric reformulation as multisets of points. If we keep \(f=1\) but consider \(h>1\), then we are dealing with additive codes. For \(h=1\) and \(f>1\) we are confronted with linear codes w.r.t.to the \(f\)th generalized Hamming weight. So, in this paper, we generalize both concepts to one more general structure. Due to this general setting, one cannot expect to determine these number in full generality. While we have some results on the asymptotic behavior, even the question for the right order of magnitude remains open in most cases. Besides a few general insights we mostly focused on \(n_q(5,2,2;s)\) and \(b_q(5,2,2;s)\), where we mostly assume \(q\in \{2,3\}\). As a first specific open problem we ask for the right order of magnitude of \(n_q(5,2,2;2)\) in terms of \(q\).

In Theorem 6 we have fully determined the minimum number \(b_2(5,2,2;s)\) of lines in \(\mathrm{PG}(4,2)\) such that each plane contains at least \(s\) elements as a function of \(s\). However, this result is still based on integer linear programming computations and we propose it as an open problem to replace some of these by theoretical lower bounds. The techniques used in [2], [4] may serve as a blueprint. If we restrict the maximum multiplicity of the lines, then in most cases we only presented upper bounds by listing explicit examples found by ILP searches. It would be interesting to determine the exact values. For \(b_3(5,2,2;s)\) we have presented partial results, see Table ¿tbl:table95b953955952952?.

In Theorem 8 we have fully determined \(n_q(5,2,2;t\cdot[3]_q+q^2+q)\). The underlying construction fits into the framework of Lemma 6: starting from the set of all lines in \(\mathrm{PG}(4,q)\) we can remove any set of lines that blocks all planes to obtain a lower bound for \(n_q(5,2,2;q^2+q)\). Choosing the trivial blocking set consisting of all \(\genfrac{[}{]}{0pt}{}{4}{2}_{q}=q^4+q^3+q^2+q+1\) lines in a solid yields \(n_q(5,2,2;q^2+q)\ge q^6+q^5+q^4+q^3\), i.e.\(n_2(5,2,2;6)\ge 120\). Choosing the blocking set obtained from the \(q^4+q^3+q^2+q+1\) lines in the orbit of a Singer-cycle of \(\mathrm{PG}(4,q)\) yields \(n_q(5,2,2;q^2+q)\ge q^6+q^5+q^4+q^3+q^2\), i.e.\(n_2(5,2,2;6)\ge 124\). The best choice of the blocking set yields the lower bound from Theorem 8, i.e.\(n_2(5,2,2;6)\ge 128\), which is tight. So far, all of our lower bounds for \(n_2(5,2,2;s)\) are of this type. Finding a good lower bound for \(n_q(5,2,2;2)\) seems to be a challenging problem.

While there is a Griesmer type bound for linear and additive codes that determines \(n_q(r,h,1;s)\) for all sufficiently large values of \(s\), we currently do not know such a bound for the cases \(h,f\ge 2\).

In order to turn the determination of \(n_q(5,2,2;s)\) and \(b_q(5,2,2;s)\) as a function of \(s\), given some fixed field size \(q\), into a finite computational problem, we have presented Lemma 23 and Lemma 19. Both bounds are generalized to some extent, but still do not cover the whole parameter space of \((r,h,f)\). We can conclude that in this paper, we give a new, rather general research direction, in which many things can still be investigated.

Acknowledgements↩︎

The authors would like to thank Timothy Alderson, Simeon Ball, and Tabriz Popatia for the discussions on additive codes during the seventh Irsee conference. There, we uncovered the relation between the geometric objects we study in this paper, and additive codes with respect to the generalized Hamming weight. Both authors discussed the initial ideas for this paper at that conference.

9 Explicit lists of blocking sets found via ILP searches↩︎

In this section we collect a list of interesting blocking sets that we have found by integer linear programming computations using the ILOG CPLEX solver without any symmetry reductions or specific settings. Some of these examples show that there are no uniqueness results for certain parameters. Others have larger cardinalities than the optimum blocking sets but require a smaller maximum line multiplicity. For each example we state an explicit list of generator matrices of all involved subspaces.

A blocking set attaining cardinality \(b_2(5,2,2;3)=75\) with maximum line multiplicity \(3\) is given by: \(\left(\begin{smallmatrix}00010\\00001\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}00010\\00001\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}00010\\00001\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}01000\\00100\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}01001\\00100\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}01001\\00101\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}01000\\00110\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}01000\\00110\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}01001\\00110\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}01010\\00101\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}01011\\00100\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}01011\\00101\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}01010\\00111\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}01010\\00111\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}01011\\00111\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}10000\\00100\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}10001\\00100\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}10001\\00101\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}10000\\00110\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}10000\\00110\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}10001\\00110\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}10010\\00101\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}10011\\00100\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}10011\\00101\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}10010\\00111\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}10010\\00111\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}10011\\00111\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}10000\\01000\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}10001\\01001\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}10010\\01010\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}10011\\01011\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}10000\\01100\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}10001\\01100\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}10001\\01101\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}10000\\01110\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}10000\\01110\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}10001\\01111\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}10010\\01101\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}10010\\01101\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}10011\\01100\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}10010\\01111\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}10011\\01110\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}10011\\01111\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}10100\\01000\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}10100\\01001\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}10101\\01001\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}10100\\01011\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}10101\\01010\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}10101\\01010\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}10110\\01000\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}10110\\01000\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}10111\\01001\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}10110\\01011\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}10111\\01010\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}10111\\01011\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}10100\\01100\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}10101\\01101\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}10110\\01110\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}10111\\01111\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}11000\\00001\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}11000\\00010\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}11000\\00011\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}11001\\00010\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}11001\\00010\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}11001\\00010\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}11001\\00011\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}11001\\00011\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}11001\\00011\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}11010\\00001\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}11010\\00001\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}11010\\00001\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}11000\\00100\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}11000\\00101\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}11000\\00110\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}11000\\00111\\\end{smallmatrix}\right)\).

A blocking set attaining cardinality \(b_2(5,2,2;3)=75\) with maximum line multiplicity \(2\) is given by: \(\left(\begin{smallmatrix}00010\\00001\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}00010\\00001\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}00101\\00010\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}01000\\00011\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}01000\\00100\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}01000\\00100\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}01001\\00101\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}01001\\00110\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}01001\\00111\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}01010\\00100\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}01010\\00101\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}01010\\00111\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}01011\\00110\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}01011\\00110\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}01110\\00001\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}10000\\00011\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}10001\\00101\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}10000\\00110\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}10001\\00110\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}10010\\00100\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}10011\\00100\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}10010\\00111\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}10100\\00001\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}10100\\00001\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}10100\\00010\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}10100\\00011\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}10101\\00010\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}10101\\00011\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}10110\\00001\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}10000\\01000\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}10000\\01001\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}10000\\01011\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}10001\\01010\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}10001\\01011\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}10010\\01000\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}10010\\01001\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}10011\\01000\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}10011\\01010\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}10011\\01011\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}10000\\01101\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}10001\\01101\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}10001\\01101\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}10000\\01111\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}10001\\01111\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}10010\\01100\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}10010\\01100\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}10011\\01100\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}10010\\01110\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}10011\\01110\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}10101\\01001\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}10100\\01010\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}10110\\01000\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}10110\\01001\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}10111\\01010\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}10111\\01011\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}10100\\01111\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}10101\\01110\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}10110\\01100\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}10111\\01101\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}10110\\01111\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}10111\\01110\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}11000\\00001\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}11000\\00010\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}11000\\00011\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}11000\\00101\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}11001\\00100\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}11000\\00111\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}11001\\00110\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}11010\\00100\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}11010\\00101\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}11011\\00101\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}11010\\00110\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}11010\\00111\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}11011\\00111\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}11101\\00010\\\end{smallmatrix}\right)\).

\(b_2(5,2,2;4,1)\le 102\): \(\left(\begin{smallmatrix}00100\\00011\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}00101\\00010\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}00101\\00011\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}00110\\00001\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}01000\\00011\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}01001\\00010\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}01001\\00011\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}01010\\00001\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}01000\\00100\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}01000\\00101\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}01001\\00100\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}01001\\00101\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}01000\\00110\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}01000\\00111\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}01001\\00111\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}01010\\00100\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}01011\\00100\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}01011\\00101\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}01011\\00110\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}01011\\00111\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}01100\\00001\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}01100\\00010\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}01100\\00011\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}01101\\00010\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}01101\\00011\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}10000\\00011\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}10001\\00010\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}10001\\00011\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}10010\\00001\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}10000\\00101\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}10001\\00100\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}10001\\00101\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}10000\\00110\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}10001\\00110\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}10010\\00100\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}10010\\00101\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}10010\\00110\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}10010\\00111\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}10011\\00110\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}10011\\00111\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}10100\\00001\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}10100\\00010\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}10100\\00011\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}10101\\00011\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}10110\\00001\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}10000\\01000\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}10000\\01001\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}10001\\01000\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}10000\\01010\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}10001\\01010\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}10010\\01000\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}10010\\01001\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}10011\\01000\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}10011\\01001\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}10011\\01010\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}10000\\01101\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}10001\\01101\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}10000\\01110\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}10000\\01111\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}10001\\01110\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}10010\\01100\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}10010\\01111\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}10011\\01111\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}10100\\01000\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}10101\\01000\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}10101\\01010\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}10110\\01000\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}10111\\01001\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}10110\\01010\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}10110\\01011\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}10111\\01010\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}10111\\01011\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}10100\\01100\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}10100\\01101\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}10101\\01101\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}10100\\01111\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}10101\\01111\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}10110\\01100\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}10111\\01100\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}10110\\01110\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}10111\\01110\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}10111\\01111\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}11000\\00001\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}11000\\00010\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}11001\\00010\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}11010\\00001\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}11000\\00101\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}11001\\00101\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}11000\\00110\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}11000\\00111\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}11001\\00110\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}11001\\00111\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}11010\\00100\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}11010\\00101\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}11011\\00100\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}11011\\00101\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}11010\\00111\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}11011\\00111\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}11100\\00001\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}11100\\00010\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}11101\\00010\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}11110\\00001\\\end{smallmatrix}\right)\).

\(b_2(5,2,2;4,2)\le 98\): \(\left(\begin{smallmatrix}00101\\00010\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}00110\\00001\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}00101\\00011\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}01000\\00001\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}01100\\00011\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}01000\\00010\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}01100\\00001\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}01000\\00011\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}01100\\00010\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}01000\\00101\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}01011\\00111\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}01001\\00100\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}01001\\00100\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}01011\\00100\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}01011\\00100\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}01001\\00101\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}01000\\00111\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}01000\\00110\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}01010\\00110\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}01010\\00100\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}01010\\00100\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}10000\\00001\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}10000\\00011\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}10000\\00010\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}10000\\00101\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}10000\\00111\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}10001\\00100\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}10001\\00100\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}10011\\00100\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}10011\\00100\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}10001\\00101\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}10011\\00111\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}10000\\00110\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}10010\\00100\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}10010\\00100\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}10010\\00110\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}10100\\00001\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}10100\\00011\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}10100\\00010\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}10000\\01000\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}10000\\01100\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}10001\\01010\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}10011\\01101\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}10001\\01011\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}10001\\01011\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}10011\\01110\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}10011\\01110\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}10010\\01001\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}10010\\01001\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}10001\\01111\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}10001\\01111\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}10011\\01001\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}10010\\01111\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}10010\\01011\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}10001\\01110\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}10011\\01010\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}10011\\01010\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}10010\\01101\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}10010\\01101\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}10100\\01000\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}10100\\01100\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}10101\\01010\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}10111\\01101\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}10101\\01011\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}10101\\01011\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}10111\\01110\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}10111\\01110\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}10110\\01001\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}10110\\01001\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}10101\\01111\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}10101\\01111\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}10111\\01001\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}10110\\01111\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}10110\\01011\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}10101\\01110\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}10111\\01010\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}10111\\01010\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}10110\\01101\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}10110\\01101\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}11000\\00001\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}11100\\00011\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}11000\\00010\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}11100\\00001\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}11000\\00011\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}11100\\00010\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}11000\\00101\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}11011\\00111\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}11001\\00100\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}11001\\00100\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}11011\\00100\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}11011\\00100\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}11001\\00101\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}11000\\00111\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}11000\\00110\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}11010\\00110\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}11010\\00100\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}11010\\00100\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}00010\\00001\\\end{smallmatrix}\right)\). There are \(21\) lines of multiplicity \(2\) and \(56\) lines of multiplicity \(1\).

\(b_2(5,2,2;5,1)\le 123\): \(\left(\begin{smallmatrix}00010\\00001\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}00100\\00001\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}00100\\00010\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}00101\\00010\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}00101\\00011\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}01000\\00001\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}01000\\00010\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}01000\\00011\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}01001\\00010\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}01001\\00011\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}01010\\00001\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}01000\\00100\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}01001\\00100\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}01000\\00110\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}01000\\00111\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}01001\\00111\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}01010\\00100\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}01010\\00101\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}01010\\00110\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}01011\\00110\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}01011\\00111\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}01100\\00001\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}01100\\00010\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}01100\\00011\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}01101\\00010\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}01101\\00011\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}01110\\00001\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}10000\\00001\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}10000\\00010\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}10000\\00011\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}10001\\00010\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}10001\\00011\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}10010\\00001\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}10000\\00100\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}10000\\00101\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}10001\\00100\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}10001\\00101\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}10000\\00110\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}10000\\00111\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}10001\\00111\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}10010\\00100\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}10010\\00101\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}10011\\00100\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}10011\\00101\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}10010\\00110\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}10011\\00110\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}10011\\00111\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}10100\\00001\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}10100\\00010\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}10101\\00011\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}10110\\00001\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}10000\\01000\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}10000\\01001\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}10001\\01000\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}10001\\01001\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}10000\\01010\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}10000\\01011\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}10001\\01010\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}10010\\01001\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}10011\\01000\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}10011\\01001\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}10010\\01010\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}10010\\01011\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}10011\\01010\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}10011\\01011\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}10000\\01100\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}10001\\01101\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}10000\\01111\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}10001\\01110\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}10001\\01111\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}10010\\01101\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}10011\\01100\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}10011\\01101\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}10010\\01110\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}10010\\01111\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}10011\\01110\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}10011\\01111\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}10100\\01001\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}10101\\01000\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}10100\\01011\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}10101\\01010\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}10101\\01011\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}10110\\01000\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}10111\\01000\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}10111\\01001\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}10110\\01010\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}10110\\01011\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}10111\\01010\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}10111\\01011\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}10100\\01100\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}10100\\01101\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}10101\\01100\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}10101\\01101\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}10100\\01110\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}10101\\01110\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}10101\\01111\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}10110\\01100\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}10111\\01100\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}10111\\01101\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}10110\\01111\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}10111\\01111\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}11000\\00001\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}11000\\00011\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}11001\\00010\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}11001\\00011\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}11000\\00101\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}11001\\00101\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}11000\\00110\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}11000\\00111\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}11001\\00110\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}11001\\00111\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}11010\\00100\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}11010\\00101\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}11011\\00100\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}11011\\00101\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}11010\\00110\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}11010\\00111\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}11011\\00110\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}11011\\00111\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}11100\\00001\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}11100\\00010\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}11100\\00011\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}11101\\00011\\\end{smallmatrix}\right)\).

\(b_2(5,2,2;5,3)\le 121\): \(\left(\begin{smallmatrix}00010\\00001\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}00010\\00001\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}00010\\00001\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}00100\\00001\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}00100\\00010\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}01000\\00001\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}01000\\00011\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}01001\\00010\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}01001\\00011\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}01000\\00100\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}01000\\00101\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}01001\\00100\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}01001\\00101\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}01000\\00110\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}01000\\00111\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}01001\\00110\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}01001\\00111\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}01010\\00100\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}01010\\00101\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}01011\\00100\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}01011\\00101\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}01010\\00110\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}01010\\00111\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}01011\\00110\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}01011\\00111\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}01100\\00001\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}01101\\00010\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}10000\\00010\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}10010\\00001\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}10000\\00100\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}10000\\00101\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}10001\\00100\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}10001\\00101\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}10000\\00110\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}10000\\00111\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}10001\\00110\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}10001\\00111\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}10010\\00100\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}10010\\00101\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}10011\\00100\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}10011\\00101\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}10010\\00110\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}10010\\00111\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}10011\\00110\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}10011\\00111\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}10100\\00010\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}10100\\00011\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}10101\\00011\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}10110\\00001\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}10000\\01000\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}10000\\01001\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}10001\\01000\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}10001\\01001\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}10000\\01010\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}10000\\01011\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}10001\\01010\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}10001\\01011\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}10010\\01000\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}10010\\01001\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}10011\\01000\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}10011\\01001\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}10010\\01010\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}10010\\01011\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}10011\\01010\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}10011\\01011\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}10000\\01100\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}10001\\01100\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}10001\\01101\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}10000\\01110\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}10001\\01111\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}10010\\01110\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}10011\\01110\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}10011\\01111\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}10101\\01000\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}10100\\01010\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}10101\\01011\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}10111\\01010\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}10100\\01100\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}10100\\01101\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}10101\\01100\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}10101\\01101\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}10100\\01110\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}10100\\01111\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}10101\\01110\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}10101\\01111\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}10110\\01100\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}10110\\01101\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}10111\\01100\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}10111\\01101\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}10110\\01110\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}10110\\01111\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}10111\\01110\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}10111\\01111\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}11001\\00010\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}11010\\00001\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}11001\\00100\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}11000\\00111\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}11001\\00110\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}11010\\00100\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}11010\\00101\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}11011\\00100\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}11011\\00101\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}11011\\00110\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}11100\\00001\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}11100\\00001\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}11100\\00001\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}11100\\00010\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}11100\\00010\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}11100\\00010\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}11100\\00011\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}11100\\00011\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}11100\\00011\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}11101\\00010\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}11101\\00010\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}11101\\00010\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}11101\\00011\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}11101\\00011\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}11101\\00011\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}11110\\00001\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}11110\\00001\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}11110\\00001\\\end{smallmatrix}\right)\). The seven lines of multiplicity \(3\) are the lines contained in a plane \(\pi\). The \(48\) lines of multiplicity \(0\) intersect \(\pi\) in a point and there are no lines of multiplicity \(2\).

\(b_2(5,2,2;5,4)\le 120\): \(\left(\begin{smallmatrix}00010\\00001\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}00010\\00001\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}00010\\00001\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}00010\\00001\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}00101\\00011\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}01001\\00011\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}01000\\00100\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}01000\\00101\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}01001\\00100\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}01001\\00101\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}01000\\00110\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}01000\\00111\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}01001\\00110\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}01001\\00111\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}01010\\00100\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}01010\\00101\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}01011\\00100\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}01011\\00101\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}01010\\00110\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}01010\\00111\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}01011\\00110\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}01011\\00111\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}01100\\00001\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}01100\\00010\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}01100\\00011\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}01101\\00010\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}01101\\00011\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}01110\\00001\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}10000\\00001\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}10000\\00001\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}10000\\00001\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}10000\\00001\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}10000\\00010\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}10000\\00010\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}10000\\00010\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}10000\\00010\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}10000\\00011\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}10000\\00011\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}10000\\00011\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}10000\\00011\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}10001\\00010\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}10001\\00010\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}10001\\00010\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}10001\\00010\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}10001\\00011\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}10001\\00011\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}10001\\00011\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}10001\\00011\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}10010\\00001\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}10010\\00001\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}10010\\00001\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}10010\\00001\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}10001\\00100\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}10001\\00111\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}10010\\00100\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}10010\\00111\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}10100\\00011\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}10000\\01000\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}10000\\01011\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}10011\\01000\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}10011\\01011\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}10100\\01000\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}10100\\01001\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}10100\\01001\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}10101\\01000\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}10101\\01001\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}10100\\01010\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}10100\\01010\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}10100\\01011\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}10101\\01010\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}10101\\01011\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}10110\\01000\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}10110\\01001\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}10111\\01000\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}10111\\01001\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}10111\\01001\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}10110\\01010\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}10110\\01011\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}10111\\01010\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}10111\\01010\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}10111\\01011\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}10100\\01100\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}10100\\01101\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}10101\\01100\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}10101\\01101\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}10100\\01110\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}10100\\01111\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}10101\\01110\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}10101\\01111\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}10110\\01100\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}10110\\01101\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}10111\\01100\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}10111\\01101\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}10110\\01110\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}10110\\01111\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}10111\\01110\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}10111\\01111\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}11001\\00011\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}11000\\00100\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}11000\\00101\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}11001\\00100\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}11001\\00101\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}11001\\00101\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}11000\\00110\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}11000\\00111\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}11001\\00110\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}11001\\00110\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}11001\\00111\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}11010\\00100\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}11010\\00101\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}11010\\00101\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}11011\\00100\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}11011\\00101\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}11010\\00110\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}11010\\00110\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}11010\\00111\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}11011\\00110\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}11011\\00111\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}11100\\00011\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}11101\\00011\\\end{smallmatrix}\right)\). The seven lines of multiplicity \(4\) are the lines of a plane \(\pi\). The eight lines of multiplicity \(2\) are disjoint to \(\pi\) and the \(64\) lines of multiplicity \(0\) intersect \(\pi\) in a point.

The complement of a partial line spread of size \(9\) gives \(b_2(5,2,2;6,1)\le 146\): \(\left(\begin{smallmatrix}00010\\00001\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}00100\\00001\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}00100\\00010\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}00100\\00011\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}00101\\00010\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}00101\\00011\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}00110\\00001\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}01000\\00001\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}01000\\00010\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}01001\\00010\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}01001\\00011\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}01010\\00001\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}01000\\00100\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}01000\\00101\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}01001\\00100\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}01001\\00101\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}01000\\00110\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}01000\\00111\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}01001\\00110\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}01001\\00111\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}01010\\00100\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}01010\\00101\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}01011\\00100\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}01011\\00101\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}01010\\00110\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}01010\\00111\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}01011\\00110\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}01011\\00111\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}01100\\00001\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}01100\\00010\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}01100\\00011\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}01101\\00010\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}01101\\00011\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}10000\\00001\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}10000\\00010\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}10000\\00011\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}10001\\00010\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}10001\\00011\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}10010\\00001\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}10000\\00100\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}10000\\00101\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}10001\\00100\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}10001\\00101\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}10000\\00110\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}10000\\00111\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}10001\\00110\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}10001\\00111\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}10010\\00100\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}10011\\00100\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}10011\\00101\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}10010\\00110\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}10010\\00111\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}10011\\00110\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}10011\\00111\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}10100\\00001\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}10100\\00011\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}10101\\00010\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}10101\\00011\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}10110\\00001\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}10000\\01000\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}10000\\01001\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}10001\\01000\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}10000\\01011\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}10001\\01010\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}10001\\01011\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}10010\\01000\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}10010\\01001\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}10011\\01000\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}10011\\01001\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}10010\\01010\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}10010\\01011\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}10011\\01010\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}10011\\01011\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}10000\\01100\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}10000\\01101\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}10001\\01100\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}10001\\01101\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}10000\\01110\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}10000\\01111\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}10001\\01110\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}10001\\01111\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}10010\\01100\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}10010\\01101\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}10011\\01101\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}10010\\01110\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}10010\\01111\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}10011\\01110\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}10011\\01111\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}10100\\01000\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}10100\\01001\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}10101\\01000\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}10101\\01001\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}10100\\01010\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}10100\\01011\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}10101\\01010\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}10101\\01011\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}10110\\01000\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}10110\\01001\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}10111\\01000\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}10111\\01001\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}10110\\01010\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}10110\\01011\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}10111\\01010\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}10111\\01011\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}10100\\01100\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}10100\\01101\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}10101\\01100\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}10101\\01101\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}10100\\01110\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}10100\\01111\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}10101\\01110\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}10101\\01111\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}10110\\01100\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}10110\\01101\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}10111\\01100\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}10111\\01101\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}10110\\01110\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}10110\\01111\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}10111\\01110\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}10111\\01111\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}11000\\00001\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}11000\\00010\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}11000\\00011\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}11001\\00010\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}11001\\00011\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}11010\\00001\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}11000\\00100\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}11000\\00101\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}11001\\00101\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}11000\\00110\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}11000\\00111\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}11001\\00110\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}11001\\00111\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}11010\\00100\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}11010\\00101\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}11011\\00100\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}11011\\00101\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}11010\\00110\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}11010\\00111\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}11011\\00110\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}11100\\00001\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}11100\\00010\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}11100\\00011\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}11101\\00010\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}11101\\00011\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}11110\\00001\\\end{smallmatrix}\right)\).

\(b_2(5,2,2;6,2)\le 144\): \(\left(\begin{smallmatrix}00100\\00010\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}00100\\00011\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}00101\\00010\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}00101\\00011\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}01000\\00010\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}01000\\00011\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}01001\\00010\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}01001\\00011\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}01000\\00110\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}01000\\00111\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}01001\\00110\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}01001\\00111\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}01010\\00100\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}01011\\00100\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}01010\\00101\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}01011\\00101\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}01010\\00110\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}01011\\00111\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}01010\\00111\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}01011\\00110\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}01100\\00010\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}01100\\00011\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}01101\\00010\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}01101\\00011\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}10000\\00010\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}10000\\00011\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}10001\\00010\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}10001\\00011\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}10000\\00110\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}10000\\00111\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}10001\\00110\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}10001\\00111\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}10010\\00100\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}10010\\00100\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}10011\\00100\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}10011\\00100\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}10010\\00110\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}10011\\00111\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}10010\\00111\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}10011\\00110\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}10100\\00010\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}10100\\00011\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}10101\\00010\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}10101\\00011\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}10001\\01010\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}10001\\01011\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}10010\\01000\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}10011\\01000\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}10010\\01001\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}10011\\01001\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}10010\\01010\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}10011\\01011\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}10010\\01011\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}10011\\01010\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}10000\\01110\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}10000\\01111\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}10010\\01100\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}10011\\01100\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}10010\\01101\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}10011\\01101\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}10010\\01110\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}10011\\01111\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}10010\\01111\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}10011\\01110\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}10100\\01010\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}10100\\01011\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}10101\\01010\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}10101\\01011\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}10110\\01000\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}10111\\01000\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}10110\\01001\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}10111\\01001\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}10110\\01010\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}10111\\01011\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}10110\\01011\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}10111\\01010\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}10100\\01110\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}10100\\01111\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}10101\\01110\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}10101\\01111\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}10110\\01100\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}10111\\01100\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}10110\\01101\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}10111\\01101\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}10110\\01110\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}10111\\01111\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}10110\\01111\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}10111\\01110\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}11000\\00010\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}11000\\00011\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}11001\\00010\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}11001\\00011\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}11000\\00110\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}11000\\00111\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}11001\\00110\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}11001\\00111\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}11010\\00101\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}11011\\00101\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}11010\\00110\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}11011\\00111\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}11010\\00111\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}11011\\00110\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}11100\\00010\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}11100\\00011\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}11101\\00010\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}11101\\00011\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}00100\\00001\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}00100\\00001\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}01000\\00001\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}01010\\00001\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}01000\\00101\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}01001\\00101\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}01100\\00001\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}01110\\00001\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}10000\\00001\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}10000\\00001\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}10000\\00100\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}10000\\00100\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}10000\\00101\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}10001\\00100\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}10001\\00100\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}10001\\00101\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}10100\\00001\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}10100\\00001\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}10000\\01000\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}10000\\01001\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}10001\\01000\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}10001\\01001\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}10000\\01100\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}10000\\01101\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}10001\\01100\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}10001\\01101\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}10100\\01000\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}10100\\01001\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}10101\\01100\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}10101\\01101\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}11000\\00001\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}11010\\00001\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}11000\\00100\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}11000\\00101\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}11001\\00100\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}11001\\00101\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}11100\\00001\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}11110\\00001\\\end{smallmatrix}\right)\). Five of the seven lines of multiplicity \(2\) are contained in a plane.

\(b_2(5,2,2;6,3)\le 142\): \(\left(\begin{smallmatrix}00010\\00001\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}00010\\00001\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}00010\\00001\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}00100\\00001\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}00110\\00001\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}00110\\00001\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}01000\\00001\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}01000\\00010\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}01000\\00011\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}01001\\00010\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}01001\\00011\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}01010\\00001\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}01000\\00100\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}01000\\00101\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}01001\\00100\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}01001\\00101\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}01000\\00110\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}01000\\00111\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}01001\\00110\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}01001\\00111\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}01010\\00100\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}01010\\00101\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}01011\\00100\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}01011\\00101\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}01010\\00110\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}01010\\00111\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}01011\\00110\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}01011\\00111\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}01100\\00010\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}01100\\00011\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}01101\\00010\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}01101\\00011\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}10000\\00001\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}10000\\00001\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}10000\\00001\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}10000\\00010\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}10000\\00010\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}10000\\00010\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}10000\\00011\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}10000\\00011\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}10000\\00011\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}10001\\00010\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}10001\\00010\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}10001\\00010\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}10001\\00011\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}10001\\00011\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}10001\\00011\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}10010\\00001\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}10010\\00001\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}10010\\00001\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}10000\\00100\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}10000\\00101\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}10001\\00100\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}10001\\00101\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}10010\\00100\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}10010\\00101\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}10011\\00100\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}10011\\00101\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}10100\\00001\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}10100\\00010\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}10100\\00011\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}10101\\00010\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}10101\\00011\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}10110\\00001\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}10000\\01010\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}10000\\01011\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}10001\\01010\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}10001\\01011\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}10010\\01000\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}10010\\01001\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}10011\\01000\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}10011\\01001\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}10000\\01100\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}10000\\01101\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}10001\\01100\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}10001\\01101\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}10010\\01110\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}10010\\01111\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}10011\\01110\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}10011\\01111\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}10100\\01000\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}10100\\01001\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}10101\\01000\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}10101\\01001\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}10100\\01010\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}10100\\01011\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}10101\\01010\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}10101\\01011\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}10110\\01000\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}10110\\01001\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}10111\\01000\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}10111\\01001\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}10110\\01010\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}10110\\01011\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}10111\\01010\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}10111\\01011\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}10100\\01100\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}10100\\01101\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}10101\\01100\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}10101\\01101\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}10100\\01110\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}10100\\01111\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}10101\\01110\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}10101\\01111\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}10110\\01100\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}10110\\01101\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}10111\\01100\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}10111\\01101\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}10110\\01110\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}10110\\01111\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}10111\\01110\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}10111\\01111\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}11000\\00001\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}11000\\00001\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}11010\\00001\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}11000\\00100\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}11000\\00101\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}11001\\00100\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}11001\\00101\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}11000\\00110\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}11000\\00110\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}11000\\00110\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}11000\\00111\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}11000\\00111\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}11000\\00111\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}11001\\00110\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}11001\\00110\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}11001\\00110\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}11001\\00111\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}11001\\00111\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}11001\\00111\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}11010\\00100\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}11010\\00101\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}11011\\00100\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}11011\\00101\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}11010\\00110\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}11010\\00111\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}11011\\00110\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}11011\\00111\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}11110\\00001\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}11110\\00001\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}11110\\00001\\\end{smallmatrix}\right)\).

\(b_2(5,2,2;6,5)\le 141\): \(\left(\begin{smallmatrix}00010\\00001\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}00100\\00010\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}00100\\00011\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}00101\\00010\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}00101\\00011\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}00110\\00001\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}01000\\00001\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}01000\\00010\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}01000\\00011\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}01001\\00010\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}01001\\00011\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}01000\\00100\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}01000\\00101\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}01001\\00100\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}01001\\00101\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}01000\\00110\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}01001\\00111\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}01010\\00101\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}01010\\00101\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}01011\\00100\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}01011\\00100\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}01010\\00110\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}01010\\00111\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}01011\\00110\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}01011\\00111\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}01100\\00001\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}01100\\00010\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}01101\\00010\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}01101\\00011\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}01110\\00001\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}01110\\00001\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}10000\\00001\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}10000\\00010\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}10000\\00011\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}10001\\00011\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}10010\\00001\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}10010\\00001\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}10000\\00100\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}10000\\00101\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}10001\\00100\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}10001\\00101\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}10000\\00110\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}10000\\00111\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}10001\\00110\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}10001\\00111\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}10011\\00100\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}10011\\00100\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}10011\\00101\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}10011\\00101\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}10010\\00110\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}10010\\00111\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}10100\\00001\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}10100\\00010\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}10100\\00011\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}10101\\00010\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}10101\\00011\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}10000\\01000\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}10000\\01001\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}10001\\01000\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}10001\\01001\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}10000\\01010\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}10000\\01011\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}10001\\01010\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}10001\\01011\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}10010\\01000\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}10010\\01001\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}10011\\01001\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}10011\\01010\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}10011\\01010\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}10011\\01011\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}10011\\01011\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}10000\\01101\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}10001\\01100\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}10000\\01110\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}10001\\01110\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}10010\\01100\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}10010\\01101\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}10010\\01110\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}10010\\01110\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}10010\\01111\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}10010\\01111\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}10011\\01110\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}10011\\01110\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}10011\\01111\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}10011\\01111\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}10011\\01111\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}10011\\01111\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}10011\\01111\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}10100\\01001\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}10101\\01000\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}10100\\01010\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}10100\\01011\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}10101\\01010\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}10101\\01011\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}10110\\01000\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}10110\\01001\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}10111\\01000\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}10111\\01001\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}10110\\01010\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}10110\\01010\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}10111\\01011\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}10111\\01011\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}10100\\01100\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}10100\\01101\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}10101\\01100\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}10101\\01101\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}10100\\01110\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}10100\\01111\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}10101\\01110\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}10110\\01100\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}10110\\01101\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}10111\\01100\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}10111\\01101\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}10110\\01111\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}10110\\01111\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}10111\\01111\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}10111\\01111\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}11000\\00010\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}11000\\00011\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}11001\\00010\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}11001\\00011\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}11010\\00001\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}11000\\00100\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}11000\\00100\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}11001\\00101\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}11001\\00101\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}11000\\00110\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}11000\\00111\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}11001\\00110\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}11001\\00111\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}11010\\00100\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}11010\\00101\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}11011\\00100\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}11011\\00101\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}11010\\00111\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}11011\\00110\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}11100\\00001\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}11100\\00001\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}11101\\00010\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}11101\\00011\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}11110\\00001\\\end{smallmatrix}\right)\). There is a unique line of multiplicity \(5\) and all other lines have multiplicity at most \(2\).

A blocking set with line multiplicity \(3\) showing \(b_3(5,2,2;5)\le 502\) is given by: \(\left(\begin{smallmatrix}00100\\00001\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}00110\\00001\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}00100\\00010\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}00100\\00010\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}00102\\00011\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}00102\\00011\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}00100\\00011\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}00100\\00011\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}00101\\00012\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}00101\\00012\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}00100\\00012\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}00100\\00012\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}00101\\00010\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}00101\\00010\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}00101\\00011\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}00101\\00011\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}00102\\00012\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}00102\\00012\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}00102\\00010\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}00102\\00010\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}00120\\00001\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}01000\\00001\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}01100\\00001\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}01010\\00001\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}01010\\00001\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}01110\\00001\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}01110\\00001\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}01020\\00001\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}01120\\00001\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}01000\\00100\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}01020\\00110\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}01000\\00101\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}01022\\00111\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}01000\\00102\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}01021\\00112\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}01001\\00100\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}01021\\00110\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}01001\\00101\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}01020\\00111\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}01001\\00102\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}01022\\00112\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}01002\\00100\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}01022\\00110\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}01002\\00101\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}01021\\00111\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}01002\\00102\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}01020\\00112\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}01000\\00120\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}01000\\00121\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}01000\\00122\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}01001\\00120\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}01001\\00121\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}01001\\00122\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}01002\\00120\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}01002\\00121\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}01002\\00122\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}01210\\00001\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}01220\\00001\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}01220\\00001\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}01200\\00001\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}10000\\00010\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}10000\\00010\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}10000\\00011\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}10000\\00011\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}10000\\00012\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}10000\\00012\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}10001\\00010\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}10001\\00010\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}10001\\00011\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}10001\\00011\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}10001\\00012\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}10001\\00012\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}10002\\00010\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}10002\\00010\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}10002\\00011\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}10002\\00011\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}10002\\00012\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}10002\\00012\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}10100\\00001\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}10100\\00001\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}10110\\00001\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}10110\\00001\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}10120\\00001\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}10120\\00001\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}10200\\00001\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}10220\\00001\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}10200\\00010\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}10201\\00011\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}10200\\00011\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}10202\\00012\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}10200\\00012\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}10201\\00010\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}10202\\00011\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}10201\\00012\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}10202\\00010\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}10210\\00001\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}10000\\01020\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}10000\\01122\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}10000\\01021\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}10000\\01120\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}10000\\01022\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}10000\\01121\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}10001\\01020\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}10001\\01122\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}10001\\01021\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}10001\\01120\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}10001\\01022\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}10001\\01121\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}10002\\01020\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}10002\\01122\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}10002\\01021\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}10002\\01120\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}10002\\01022\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}10002\\01121\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}10010\\01000\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}10011\\01100\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}10010\\01001\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}10011\\01101\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}10010\\01002\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}10011\\01102\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}10011\\01000\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}10012\\01100\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}10011\\01001\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}10012\\01101\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}10011\\01002\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}10012\\01102\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}10012\\01000\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}10010\\01100\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}10012\\01001\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}10010\\01101\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}10012\\01002\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}10010\\01102\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}10020\\01020\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}10022\\01122\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}10020\\01021\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}10022\\01120\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}10020\\01022\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}10022\\01121\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}10021\\01020\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}10020\\01122\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}10021\\01021\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}10020\\01120\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}10021\\01022\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}10020\\01121\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}10022\\01020\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}10021\\01122\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}10022\\01021\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}10021\\01120\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}10022\\01022\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}10021\\01121\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}10000\\01202\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}10000\\01200\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}10000\\01201\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}10001\\01202\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}10001\\01200\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}10001\\01201\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}10002\\01202\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}10002\\01200\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}10002\\01201\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}10011\\01210\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}10011\\01211\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}10011\\01212\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}10012\\01210\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}10012\\01211\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}10012\\01212\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}10010\\01210\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}10010\\01211\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}10010\\01212\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}10022\\01202\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}10022\\01200\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}10022\\01201\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}10020\\01202\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}10020\\01200\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}10020\\01201\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}10021\\01202\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}10021\\01200\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}10021\\01201\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}10110\\01010\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}10121\\01111\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}10110\\01011\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}10121\\01112\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}10110\\01012\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}10121\\01110\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}10111\\01010\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}10122\\01111\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}10111\\01011\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}10122\\01112\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}10111\\01012\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}10122\\01110\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}10112\\01010\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}10120\\01111\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}10112\\01011\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}10120\\01112\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}10112\\01012\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}10120\\01110\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}10110\\01020\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}10121\\01122\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}10110\\01021\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}10121\\01120\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}10110\\01022\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}10121\\01121\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}10111\\01020\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}10122\\01122\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}10111\\01021\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}10122\\01120\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}10111\\01022\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}10122\\01121\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}10112\\01020\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}10120\\01122\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}10112\\01021\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}10120\\01120\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}10112\\01022\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}10120\\01121\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}10120\\01010\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}10120\\01010\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}10120\\01010\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}10102\\01111\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}10102\\01111\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}10102\\01111\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}10120\\01011\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}10120\\01011\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}10120\\01011\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}10102\\01112\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}10102\\01112\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}10102\\01112\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}10120\\01012\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}10120\\01012\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}10120\\01012\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}10102\\01110\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}10102\\01110\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}10102\\01110\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}10121\\01010\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}10121\\01010\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}10121\\01010\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}10100\\01111\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}10100\\01111\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}10100\\01111\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}10121\\01011\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}10121\\01011\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}10121\\01011\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}10100\\01112\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}10100\\01112\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}10100\\01112\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}10121\\01012\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}10121\\01012\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}10121\\01012\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}10100\\01110\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}10100\\01110\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}10100\\01110\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}10122\\01010\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}10122\\01010\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}10122\\01010\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}10101\\01111\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}10101\\01111\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}10101\\01111\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}10122\\01011\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}10122\\01011\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}10122\\01011\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}10101\\01112\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}10101\\01112\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}10101\\01112\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}10122\\01012\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}10122\\01012\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}10122\\01012\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}10101\\01110\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}10101\\01110\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}10101\\01110\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}10110\\01221\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}10110\\01221\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}10110\\01221\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}10110\\01222\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}10110\\01222\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}10110\\01222\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}10110\\01220\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}10110\\01220\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}10110\\01220\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}10111\\01221\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}10111\\01221\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}10111\\01221\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}10111\\01222\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}10111\\01222\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}10111\\01222\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}10111\\01220\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}10111\\01220\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}10111\\01220\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}10112\\01221\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}10112\\01221\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}10112\\01221\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}10112\\01222\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}10112\\01222\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}10112\\01222\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}10112\\01220\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}10112\\01220\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}10112\\01220\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}10102\\01221\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}10102\\01222\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}10102\\01220\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}10100\\01221\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}10100\\01222\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}10100\\01220\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}10101\\01221\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}10101\\01222\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}10101\\01220\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}10102\\01202\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}10102\\01200\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}10102\\01201\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}10100\\01202\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}10100\\01200\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}10100\\01201\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}10101\\01202\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}10101\\01200\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}10101\\01201\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}10200\\01000\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}10220\\01100\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}10200\\01001\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}10220\\01101\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}10200\\01002\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}10220\\01102\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}10201\\01000\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}10221\\01100\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}10201\\01001\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}10221\\01101\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}10201\\01002\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}10221\\01102\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}10202\\01000\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}10222\\01100\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}10202\\01001\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}10222\\01101\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}10202\\01002\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}10222\\01102\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}10200\\01010\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}10220\\01111\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}10200\\01011\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}10220\\01112\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}10200\\01012\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}10220\\01110\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}10201\\01010\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}10221\\01111\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}10201\\01011\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}10221\\01112\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}10201\\01012\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}10221\\01110\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}10202\\01010\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}10222\\01111\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}10202\\01011\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}10222\\01112\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}10202\\01012\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}10222\\01110\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}10200\\01020\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}10220\\01122\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}10200\\01021\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}10220\\01120\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}10200\\01022\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}10220\\01121\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}10201\\01020\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}10221\\01122\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}10201\\01021\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}10221\\01120\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}10201\\01022\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}10221\\01121\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}10202\\01020\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}10222\\01122\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}10202\\01021\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}10222\\01120\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}10202\\01022\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}10222\\01121\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}10220\\01000\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}10212\\01100\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}10220\\01001\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}10212\\01101\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}10220\\01002\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}10212\\01102\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}10221\\01000\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}10210\\01100\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}10221\\01001\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}10210\\01101\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}10221\\01002\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}10210\\01102\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}10222\\01000\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}10211\\01100\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}10222\\01001\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}10211\\01101\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}10222\\01002\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}10211\\01102\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}10201\\01210\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}10201\\01211\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}10201\\01212\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}10202\\01210\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}10202\\01211\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}10202\\01212\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}10200\\01210\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}10200\\01211\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}10200\\01212\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}10212\\01210\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}10212\\01211\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}10212\\01212\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}10210\\01210\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}10210\\01211\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}10210\\01212\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}10211\\01210\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}10211\\01211\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}10211\\01212\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}10212\\01221\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}10212\\01222\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}10212\\01220\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}10210\\01221\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}10210\\01222\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}10210\\01220\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}10211\\01221\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}10211\\01222\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}10211\\01220\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}10212\\01202\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}10212\\01200\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}10212\\01201\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}10210\\01202\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}10210\\01200\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}10210\\01201\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}10211\\01202\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}10211\\01200\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}10211\\01201\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}11000\\00001\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}11000\\00001\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}11100\\00001\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}11100\\00001\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}11010\\00001\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}11110\\00001\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}11020\\00001\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}11120\\00001\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}11010\\00110\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}11020\\00121\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}11010\\00111\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}11022\\00122\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}11010\\00112\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}11021\\00120\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}11011\\00110\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}11021\\00121\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}11011\\00111\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}11020\\00122\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}11011\\00112\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}11022\\00120\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}11012\\00110\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}11022\\00121\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}11012\\00111\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}11021\\00122\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}11012\\00112\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}11020\\00120\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}11020\\00100\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}11020\\00101\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}11020\\00102\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}11021\\00100\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}11021\\00101\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}11021\\00102\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}11022\\00100\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}11022\\00101\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}11022\\00102\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}11210\\00001\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}11210\\00001\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}11220\\00001\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}11200\\00001\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}12000\\00001\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}12200\\00001\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}12010\\00001\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}12210\\00001\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}12020\\00001\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}12020\\00001\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}12220\\00001\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}12220\\00001\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}12000\\00100\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}12010\\00110\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}12000\\00101\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}12011\\00111\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}12000\\00102\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}12012\\00112\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}12001\\00100\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}12011\\00110\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}12001\\00101\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}12012\\00111\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}12001\\00102\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}12010\\00112\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}12002\\00100\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}12012\\00110\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}12002\\00101\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}12010\\00111\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}12002\\00102\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}12011\\00112\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}12000\\00120\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}12000\\00121\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}12000\\00122\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}12001\\00120\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}12001\\00121\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}12001\\00122\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}12002\\00120\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}12002\\00121\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}12002\\00122\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}12100\\00001\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}12110\\00001\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}12110\\00001\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}12120\\00001\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}00010\\00001\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}10000\\00001\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}10010\\00001\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}10020\\00001\\\end{smallmatrix}\right)\).

A blocking set with line multiplicity \(6\) showing \(b_3(5,2,2;6)\le 600\) is given by: \(\left(\begin{smallmatrix}00100\\00001\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}00110\\00001\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}00120\\00001\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}01000\\00001\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}01000\\00001\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}01100\\00001\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}01100\\00001\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}01010\\00001\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}01110\\00001\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}01020\\00001\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}01120\\00001\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}01000\\00110\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}01012\\00121\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}01000\\00111\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}01011\\00122\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}01000\\00112\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}01010\\00120\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}01001\\00110\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}01010\\00121\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}01001\\00111\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}01012\\00122\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}01001\\00112\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}01011\\00120\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}01002\\00110\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}01011\\00121\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}01002\\00111\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}01010\\00122\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}01002\\00112\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}01012\\00120\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}01010\\00100\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}01010\\00101\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}01010\\00102\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}01011\\00100\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}01011\\00101\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}01011\\00102\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}01012\\00100\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}01012\\00101\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}01012\\00102\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}01010\\00110\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}01020\\00121\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}01010\\00111\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}01022\\00122\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}01010\\00112\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}01021\\00120\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}01011\\00110\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}01021\\00121\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}01011\\00111\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}01020\\00122\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}01011\\00112\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}01022\\00120\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}01012\\00110\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}01022\\00121\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}01012\\00111\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}01021\\00122\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}01012\\00112\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}01020\\00120\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}01020\\00100\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}01020\\00101\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}01020\\00102\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}01021\\00100\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}01021\\00101\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}01021\\00102\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}01022\\00100\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}01022\\00101\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}01022\\00102\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}01210\\00001\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}01210\\00001\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}01220\\00001\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}01200\\00001\\\end{smallmatrix}\right)\), 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\(\left(\begin{smallmatrix}10202\\01221\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}10202\\01222\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}10202\\01220\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}10200\\01221\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}10200\\01222\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}10200\\01220\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}10201\\01202\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}10201\\01200\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}10201\\01201\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}10202\\01202\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}10202\\01200\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}10202\\01201\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}10200\\01202\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}10200\\01200\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}10200\\01201\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}11000\\00001\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}11100\\00001\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}11010\\00001\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}11010\\00001\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}11110\\00001\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}11110\\00001\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}11020\\00001\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}11120\\00001\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}11000\\00100\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}11020\\00110\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}11000\\00101\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}11022\\00111\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}11000\\00102\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}11021\\00112\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}11001\\00100\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}11021\\00110\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}11001\\00101\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}11020\\00111\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}11001\\00102\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}11022\\00112\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}11002\\00100\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}11022\\00110\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}11002\\00101\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}11021\\00111\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}11002\\00102\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}11020\\00112\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}11000\\00120\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}11000\\00121\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}11000\\00122\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}11001\\00120\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}11001\\00121\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}11001\\00122\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}11002\\00120\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}11002\\00121\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}11002\\00122\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}11010\\00110\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}11020\\00121\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}11010\\00111\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}11022\\00122\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}11010\\00112\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}11021\\00120\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}11011\\00110\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}11021\\00121\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}11011\\00111\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}11020\\00122\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}11011\\00112\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}11022\\00120\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}11012\\00110\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}11022\\00121\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}11012\\00111\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}11021\\00122\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}11012\\00112\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}11020\\00120\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}11020\\00100\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}11020\\00101\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}11020\\00102\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}11021\\00100\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}11021\\00101\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}11021\\00102\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}11022\\00100\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}11022\\00101\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}11022\\00102\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}11210\\00001\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}11220\\00001\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}11220\\00001\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}11200\\00001\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}12000\\00001\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}12200\\00001\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}12010\\00001\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}12210\\00001\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}12020\\00001\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}12020\\00001\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}12220\\00001\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}12220\\00001\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}12000\\00100\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}12010\\00110\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}12000\\00101\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}12011\\00111\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}12000\\00102\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}12012\\00112\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}12001\\00100\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}12011\\00110\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}12001\\00101\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}12012\\00111\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}12001\\00102\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}12010\\00112\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}12002\\00100\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}12012\\00110\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}12002\\00101\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}12010\\00111\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}12002\\00102\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}12011\\00112\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}12000\\00120\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}12000\\00121\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}12000\\00122\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}12001\\00120\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}12001\\00121\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}12001\\00122\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}12002\\00120\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}12002\\00121\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}12002\\00122\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}12010\\00100\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}12021\\00110\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}12010\\00101\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}12022\\00111\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}12010\\00102\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}12020\\00112\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}12011\\00100\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}12022\\00110\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}12011\\00101\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}12020\\00111\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}12011\\00102\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}12021\\00112\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}12012\\00100\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}12020\\00110\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}12012\\00101\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}12021\\00111\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}12012\\00102\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}12022\\00112\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}12010\\00120\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}12010\\00121\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}12010\\00122\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}12011\\00120\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}12011\\00121\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}12011\\00122\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}12012\\00120\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}12012\\00121\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}12012\\00122\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}12100\\00001\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}12110\\00001\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}12110\\00001\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}12120\\00001\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}00010\\00001\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}00010\\00001\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}00010\\00001\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}10000\\00001\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}10010\\00001\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}10020\\00001\\\end{smallmatrix}\right)\).

A blocking set showing \(b_3(5,2,2;2,1)\le 206\) is given by: \(\left(\begin{smallmatrix}01010\\00110\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}01011\\00111\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}01010\\00111\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}01011\\00112\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}01010\\00112\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}01011\\00110\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}01012\\00111\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}01012\\00112\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}01012\\00110\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}01020\\00100\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}01022\\00100\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}01020\\00101\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}01022\\00101\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}01020\\00102\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}01022\\00102\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}01021\\00100\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}01021\\00101\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}01021\\00102\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}10010\\00120\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}10011\\00122\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}10010\\00121\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}10011\\00120\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}10010\\00122\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}10011\\00121\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}10012\\00122\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}10012\\00120\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}10012\\00121\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}10020\\01000\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}10022\\01000\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}10020\\01001\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}10022\\01001\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}10020\\01002\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}10022\\01002\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}10021\\01000\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}10021\\01001\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}10021\\01002\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}10020\\01110\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}10022\\01111\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}10020\\01111\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}10022\\01112\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}10020\\01112\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}10022\\01110\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}10021\\01110\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}10021\\01111\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}10021\\01112\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}10000\\01210\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}10000\\01211\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}10000\\01212\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}10001\\01210\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}10001\\01211\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}10001\\01212\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}10002\\01210\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}10002\\01211\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}10002\\01212\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}10010\\01220\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}10011\\01222\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}10010\\01221\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}10011\\01220\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}10010\\01222\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}10011\\01221\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}10012\\01222\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}10012\\01220\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}10012\\01221\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}10110\\01010\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}10111\\01011\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}10110\\01011\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}10111\\01012\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}10110\\01012\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}10111\\01010\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}10112\\01011\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}10112\\01012\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}10112\\01010\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}10110\\01110\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}10111\\01111\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}10110\\01111\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}10111\\01112\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}10110\\01112\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}10111\\01110\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}10112\\01111\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}10112\\01112\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}10112\\01110\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}10120\\01100\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}10122\\01100\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}10120\\01101\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}10122\\01101\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}10120\\01102\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}10122\\01102\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}10121\\01100\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}10121\\01101\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}10121\\01102\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}10120\\01210\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}10122\\01211\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}10120\\01211\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}10122\\01212\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}10120\\01212\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}10122\\01210\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}10121\\01210\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}10121\\01211\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}10121\\01212\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}10220\\01020\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}10222\\01022\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}10220\\01021\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}10222\\01020\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}10220\\01022\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}10222\\01021\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}10221\\01020\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}10221\\01021\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}10221\\01022\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}10210\\01100\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}10211\\01100\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}10210\\01101\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}10211\\01101\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}10210\\01102\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}10211\\01102\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}10212\\01100\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}10212\\01101\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}10212\\01102\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}10210\\01200\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}10211\\01200\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}10210\\01201\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}10211\\01201\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}10210\\01202\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}10211\\01202\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}10212\\01200\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}10212\\01201\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}10212\\01202\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}11000\\00010\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}11000\\00011\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}11000\\00012\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}11001\\00010\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}11001\\00011\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}11001\\00012\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}11002\\00010\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}11002\\00011\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}11002\\00012\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}11100\\00010\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}11100\\00011\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}11100\\00012\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}11101\\00010\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}11101\\00011\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}11101\\00012\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}11102\\00010\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}11102\\00011\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}11102\\00012\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}12000\\00110\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}12000\\00111\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}12000\\00112\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}12001\\00110\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}12001\\00111\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}12001\\00112\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}12002\\00110\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}12002\\00111\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}12002\\00112\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}12010\\00120\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}12011\\00122\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}12010\\00121\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}12011\\00120\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}12010\\00122\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}12011\\00121\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}12012\\00122\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}12012\\00120\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}12012\\00121\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}00010\\00001\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}00110\\00001\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}01000\\00001\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}01010\\00001\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}01100\\00001\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}01110\\00001\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}01120\\00001\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}01200\\00001\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}10020\\00001\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}10000\\00100\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}10000\\00101\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}10000\\00102\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}10001\\00100\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}10001\\00101\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}10001\\00102\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}10002\\00100\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}10002\\00101\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}10002\\00102\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}10110\\00001\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}10120\\00001\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}10210\\00001\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}10200\\01000\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}10200\\01001\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}10200\\01002\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}10201\\01000\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}10201\\01001\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}10201\\01002\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}10202\\01000\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}10202\\01001\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}10202\\01002\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}11000\\00001\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}11010\\00001\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}11020\\00001\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}11100\\00001\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}11110\\00001\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}11120\\00001\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}11220\\00001\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}12000\\00001\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}12010\\00001\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}12020\\00001\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}12100\\00001\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}12110\\00001\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}12210\\00001\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}12220\\00001\\\end{smallmatrix}\right)\).

A blocking set showing \(b_3(5,2,2;5,1)\le 550\) is given by: \(\left(\begin{smallmatrix}00100\\00001\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}00110\\00001\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}00100\\00010\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}00102\\00011\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}00100\\00011\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}00101\\00012\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}00100\\00012\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}00101\\00010\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}00101\\00011\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}00102\\00012\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}00102\\00010\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}00120\\00001\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}01000\\00001\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}01100\\00001\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}01000\\00012\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}01100\\00010\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}01001\\00012\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}01101\\00010\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}01002\\00012\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}01102\\00010\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}01020\\00001\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}01120\\00001\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}01000\\00100\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}01020\\00110\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}01001\\00100\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}01021\\00110\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}01002\\00100\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}01022\\00110\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}01000\\00111\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}01011\\00122\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}01001\\00111\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}01012\\00122\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}01002\\00111\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}01010\\00122\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}01000\\00121\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}01001\\00121\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}01002\\00121\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}01010\\00101\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}01011\\00101\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}01012\\00101\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}01010\\00112\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}01021\\00120\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}01011\\00112\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}01022\\00120\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}01012\\00112\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}01020\\00120\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}01020\\00102\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}01021\\00102\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}01022\\00102\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}01210\\00001\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}01202\\00011\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}01200\\00011\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}01201\\00011\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}01200\\00001\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}10000\\00010\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}10000\\00011\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}10000\\00012\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}10001\\00010\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}10001\\00011\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}10001\\00012\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}10000\\00101\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}10000\\00111\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}10001\\00102\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}10001\\00112\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}10002\\00100\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}10002\\00110\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}10002\\00101\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}10002\\00111\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}10002\\00102\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}10002\\00112\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}10000\\00122\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}10001\\00120\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}10002\\00121\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}10002\\00122\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}10002\\00120\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}10010\\00100\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}10011\\00110\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}10010\\00101\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}10011\\00111\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}10011\\00101\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}10012\\00111\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}10011\\00102\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}10012\\00112\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}10012\\00100\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}10010\\00110\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}10012\\00102\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}10010\\00112\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}10011\\00121\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}10011\\00120\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}10012\\00121\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}10012\\00122\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}10010\\00122\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}10010\\00120\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}10021\\00101\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}10020\\00111\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}10022\\00122\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}10100\\00001\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}10110\\00001\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}10100\\00010\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}10102\\00011\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}10100\\00011\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}10101\\00012\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}10100\\00012\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}10101\\00010\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}10101\\00011\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}10102\\00012\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}10102\\00010\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}10120\\00001\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}10200\\00001\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}10220\\00001\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}10200\\00011\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}10202\\00012\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}10202\\00010\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}10210\\00001\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}10002\\01000\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}10002\\01100\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}10002\\01001\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}10002\\01101\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}10002\\01002\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}10002\\01102\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}10000\\01010\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}10000\\01111\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}10000\\01011\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}10000\\01112\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}10000\\01012\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}10000\\01110\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}10001\\01010\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}10001\\01111\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}10001\\01011\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}10001\\01112\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}10001\\01012\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}10001\\01110\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}10002\\01010\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}10002\\01111\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}10002\\01011\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}10002\\01112\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}10002\\01012\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}10002\\01110\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}10000\\01020\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}10000\\01122\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}10000\\01021\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}10000\\01120\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}10000\\01022\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}10000\\01121\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}10001\\01020\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}10001\\01122\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}10001\\01021\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}10001\\01120\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}10001\\01022\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}10001\\01121\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}10002\\01020\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}10002\\01122\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}10002\\01021\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}10002\\01120\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}10002\\01022\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}10002\\01121\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}10011\\01000\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}10012\\01100\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}10011\\01001\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}10012\\01101\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}10011\\01002\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}10012\\01102\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}10011\\01010\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}10012\\01111\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}10011\\01011\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}10012\\01112\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}10011\\01012\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}10012\\01110\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}10011\\01020\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}10012\\01122\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}10011\\01021\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}10012\\01120\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}10011\\01022\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}10012\\01121\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}10020\\01000\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}10022\\01100\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}10020\\01001\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}10022\\01101\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}10020\\01002\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}10022\\01102\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}10020\\01010\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}10022\\01111\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}10020\\01011\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}10022\\01112\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}10020\\01012\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}10022\\01110\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}10021\\01010\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}10020\\01111\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}10021\\01011\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}10020\\01112\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}10021\\01012\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}10020\\01110\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}10022\\01010\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}10021\\01111\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}10022\\01011\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}10021\\01112\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}10022\\01012\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}10021\\01110\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}10020\\01020\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}10022\\01122\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}10020\\01021\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}10022\\01120\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}10020\\01022\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}10022\\01121\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}10002\\01210\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}10002\\01211\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}10002\\01212\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}10000\\01221\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}10000\\01222\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}10000\\01220\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}10001\\01221\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}10001\\01222\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}10001\\01220\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}10002\\01221\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}10002\\01222\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}10002\\01220\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}10000\\01202\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}10000\\01200\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}10000\\01201\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}10001\\01202\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}10001\\01200\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}10001\\01201\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}10002\\01202\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}10002\\01200\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}10002\\01201\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}10010\\01210\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}10010\\01211\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}10010\\01212\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}10010\\01221\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}10010\\01222\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}10010\\01220\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}10010\\01202\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}10010\\01200\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}10010\\01201\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}10021\\01210\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}10021\\01211\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}10021\\01212\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}10022\\01221\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}10022\\01222\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}10022\\01220\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}10020\\01221\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}10020\\01222\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}10020\\01220\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}10021\\01221\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}10021\\01222\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}10021\\01220\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}10021\\01202\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}10021\\01200\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}10021\\01201\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}10102\\01000\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}10112\\01100\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}10102\\01001\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}10112\\01101\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}10102\\01002\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}10112\\01102\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}10100\\01010\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}10110\\01111\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}10100\\01011\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}10110\\01112\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}10100\\01012\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}10110\\01110\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}10101\\01020\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}10111\\01122\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}10101\\01021\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}10111\\01120\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}10101\\01022\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}10111\\01121\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}10110\\01000\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}10121\\01100\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}10110\\01001\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}10121\\01101\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}10110\\01002\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}10121\\01102\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}10111\\01010\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}10122\\01111\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}10111\\01011\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}10122\\01112\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}10111\\01012\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}10122\\01110\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}10112\\01020\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}10120\\01122\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}10112\\01021\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}10120\\01120\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}10112\\01022\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}10120\\01121\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}10120\\01000\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}10102\\01100\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}10120\\01001\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}10102\\01101\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}10120\\01002\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}10102\\01102\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}10121\\01010\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}10100\\01111\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}10121\\01011\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}10100\\01112\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}10121\\01012\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}10100\\01110\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}10122\\01020\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}10101\\01122\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}10122\\01021\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}10101\\01120\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}10122\\01022\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}10101\\01121\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}10112\\01210\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}10112\\01211\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}10112\\01212\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}10110\\01221\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}10110\\01222\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}10110\\01220\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}10111\\01202\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}10111\\01200\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}10111\\01201\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}10120\\01210\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}10120\\01211\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}10120\\01212\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}10121\\01221\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}10121\\01222\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}10121\\01220\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}10122\\01202\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}10122\\01200\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}10122\\01201\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}10100\\01210\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}10100\\01211\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}10100\\01212\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}10101\\01221\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}10101\\01222\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}10101\\01220\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}10102\\01202\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}10102\\01200\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}10102\\01201\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}10202\\01000\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}10222\\01100\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}10202\\01001\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}10222\\01101\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}10202\\01002\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}10222\\01102\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}10201\\01010\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}10221\\01111\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}10201\\01011\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}10221\\01112\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}10201\\01012\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}10221\\01110\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}10202\\01020\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}10222\\01122\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}10202\\01021\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}10222\\01120\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}10202\\01022\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}10222\\01121\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}10211\\01000\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}10202\\01100\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}10211\\01001\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}10202\\01101\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}10211\\01002\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}10202\\01102\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}10210\\01010\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}10201\\01111\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}10210\\01011\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}10201\\01112\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}10210\\01012\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}10201\\01110\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}10211\\01010\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}10202\\01111\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}10211\\01011\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}10202\\01112\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}10211\\01012\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}10202\\01110\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}10210\\01020\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}10201\\01122\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}10210\\01021\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}10201\\01120\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}10210\\01022\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}10201\\01121\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}10211\\01020\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}10202\\01122\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}10211\\01021\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}10202\\01120\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}10211\\01022\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}10202\\01121\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}10212\\01020\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}10200\\01122\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}10212\\01021\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}10200\\01120\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}10212\\01022\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}10200\\01121\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}10220\\01000\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}10212\\01100\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}10220\\01001\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}10212\\01101\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}10220\\01002\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}10212\\01102\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}10221\\01000\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}10210\\01100\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}10221\\01001\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}10210\\01101\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}10221\\01002\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}10210\\01102\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}10220\\01010\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}10212\\01111\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}10220\\01011\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}10212\\01112\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}10220\\01012\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}10212\\01110\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}10220\\01020\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}10212\\01122\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}10220\\01021\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}10212\\01120\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}10220\\01022\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}10212\\01121\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}10221\\01020\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}10210\\01122\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}10221\\01021\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}10210\\01120\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}10221\\01022\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}10210\\01121\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}10222\\01020\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}10211\\01122\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}10222\\01021\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}10211\\01120\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}10222\\01022\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}10211\\01121\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}10222\\01210\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}10222\\01211\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}10222\\01212\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}10221\\01221\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}10221\\01222\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}10221\\01220\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}10222\\01221\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}10222\\01222\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}10222\\01220\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}10220\\01202\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}10220\\01200\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}10220\\01201\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}10221\\01202\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}10221\\01200\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}10221\\01201\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}10222\\01202\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}10222\\01200\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}10222\\01201\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}10201\\01210\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}10201\\01211\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}10201\\01212\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}10200\\01210\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}10200\\01211\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}10200\\01212\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}10200\\01221\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}10200\\01222\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}10200\\01220\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}10201\\01202\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}10201\\01200\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}10201\\01201\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}10202\\01202\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}10202\\01200\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}10202\\01201\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}10200\\01202\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}10200\\01200\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}10200\\01201\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}10211\\01210\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}10211\\01211\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}10211\\01212\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}10210\\01221\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}10210\\01222\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}10210\\01220\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}10211\\01202\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}10211\\01200\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}10211\\01201\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}11000\\00001\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}11100\\00001\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}11000\\00010\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}11100\\00011\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}11001\\00010\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}11101\\00011\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}11002\\00010\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}11102\\00011\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}11020\\00001\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}11120\\00001\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}11000\\00100\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}11020\\00110\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}11001\\00100\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}11021\\00110\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}11002\\00100\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}11022\\00110\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}11000\\00111\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}11011\\00122\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}11001\\00111\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}11012\\00122\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}11002\\00111\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}11010\\00122\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}11000\\00121\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}11001\\00121\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}11002\\00121\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}11010\\00101\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}11011\\00101\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}11012\\00101\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}11010\\00112\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}11021\\00120\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}11011\\00112\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}11022\\00120\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}11012\\00112\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}11020\\00120\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}11020\\00102\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}11021\\00102\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}11022\\00102\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}11210\\00001\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}11201\\00012\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}11202\\00012\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}11200\\00012\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}11200\\00001\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}12000\\00001\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}12200\\00001\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}12000\\00011\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}12200\\00012\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}12001\\00011\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}12201\\00012\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}12002\\00011\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}12202\\00012\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}12010\\00001\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}12210\\00001\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}12000\\00100\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}12010\\00110\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}12001\\00100\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}12011\\00110\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}12002\\00100\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}12012\\00110\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}12000\\00111\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}12022\\00122\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}12001\\00111\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}12020\\00122\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}12002\\00111\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}12021\\00122\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}12000\\00121\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}12001\\00121\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}12002\\00121\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}12010\\00102\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}12020\\00112\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}12011\\00102\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}12021\\00112\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}12012\\00102\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}12022\\00112\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}12010\\00120\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}12011\\00120\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}12012\\00120\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}12020\\00101\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}12021\\00101\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}12022\\00101\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}12100\\00001\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}12100\\00010\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}12101\\00010\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}12102\\00010\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}12120\\00001\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}10020\\00001\\\end{smallmatrix}\right)\).

A blocking set showing \(b_3(5,2,2;6,1)\le 648\) is given by: \(\left(\begin{smallmatrix}00100\\00010\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}00102\\00011\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}00100\\00011\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}00101\\00012\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}00100\\00012\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}00101\\00010\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}01000\\00001\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}01100\\00001\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}01000\\00012\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}01100\\00010\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}01001\\00012\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}01101\\00010\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}01002\\00012\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}01102\\00010\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}01010\\00001\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}01110\\00001\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}01020\\00001\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}01120\\00001\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}01000\\00102\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}01021\\00112\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}01001\\00102\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}01022\\00112\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}01002\\00102\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}01020\\00112\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}01000\\00110\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}01012\\00121\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}01000\\00111\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}01011\\00122\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}01000\\00112\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}01010\\00120\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}01001\\00110\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}01010\\00121\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}01001\\00111\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}01012\\00122\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}01001\\00112\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}01011\\00120\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}01002\\00110\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}01011\\00121\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}01002\\00111\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}01010\\00122\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}01002\\00112\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}01012\\00120\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}01000\\00120\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}01001\\00120\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}01002\\00120\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}01010\\00100\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}01010\\00101\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}01010\\00102\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}01011\\00100\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}01011\\00101\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}01011\\00102\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}01012\\00100\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}01012\\00101\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}01012\\00102\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}01010\\00110\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}01020\\00121\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}01011\\00110\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}01021\\00121\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}01012\\00110\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}01022\\00121\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}01020\\00100\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}01021\\00100\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}01022\\00100\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}01210\\00001\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}01202\\00011\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}01200\\00011\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}01201\\00011\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}01220\\00001\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}01200\\00001\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}10000\\00010\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}10000\\00011\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}10000\\00012\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}10002\\00010\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}10002\\00011\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}10002\\00012\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}10000\\00100\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}10000\\00110\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}10001\\00101\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}10001\\00111\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}10002\\00100\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}10002\\00110\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}10002\\00101\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}10002\\00111\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}10002\\00102\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}10002\\00112\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}10000\\00121\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}10001\\00122\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}10002\\00121\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}10002\\00122\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}10002\\00120\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}10010\\00102\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}10011\\00112\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}10011\\00100\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}10012\\00110\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}10011\\00102\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}10012\\00112\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}10012\\00100\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}10010\\00110\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}10012\\00101\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}10010\\00111\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}10012\\00102\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}10010\\00112\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}10011\\00121\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}10011\\00122\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}10011\\00120\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}10012\\00120\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}10010\\00121\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}10010\\00120\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}10020\\00100\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}10022\\00110\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}10020\\00101\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}10022\\00111\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}10021\\00100\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}10020\\00110\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}10021\\00102\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}10020\\00112\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}10022\\00100\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}10021\\00110\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}10022\\00121\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}10022\\00120\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}10020\\00121\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}10021\\00121\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}10021\\00122\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}10100\\00001\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}10110\\00001\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}10101\\00011\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}10102\\00012\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}10102\\00010\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}10120\\00001\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}10200\\00011\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}10202\\00012\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}10201\\00010\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}10202\\00011\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}10201\\00012\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}10202\\00010\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}10000\\01000\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}10000\\01100\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}10000\\01001\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}10000\\01101\\\end{smallmatrix}\right)\), 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\(\left(\begin{smallmatrix}10212\\01200\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}10212\\01201\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}10210\\01202\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}10210\\01200\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}10210\\01201\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}11000\\00001\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}11100\\00001\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}11000\\00010\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}11100\\00011\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}11000\\00012\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}11100\\00010\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}11001\\00010\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}11101\\00011\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}11001\\00012\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}11101\\00010\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}11002\\00010\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}11102\\00011\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}11002\\00012\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}11102\\00010\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}11010\\00001\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}11110\\00001\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}11020\\00001\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}11120\\00001\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}11000\\00101\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}11022\\00111\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}11000\\00102\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}11021\\00112\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}11001\\00101\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}11020\\00111\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}11001\\00102\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}11022\\00112\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}11002\\00101\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}11021\\00111\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}11002\\00102\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}11020\\00112\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}11000\\00111\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}11011\\00122\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}11001\\00111\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}11012\\00122\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}11002\\00111\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}11010\\00122\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}11000\\00120\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}11000\\00122\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}11001\\00120\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}11001\\00122\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}11002\\00120\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}11002\\00122\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}11010\\00101\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}11011\\00101\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}11012\\00101\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}11010\\00110\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}11020\\00121\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}11011\\00110\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}11021\\00121\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}11012\\00110\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}11022\\00121\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}11020\\00100\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}11021\\00100\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}11022\\00100\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}11210\\00001\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}11202\\00011\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}11201\\00012\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}11200\\00011\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}11202\\00012\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}11201\\00011\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}11200\\00012\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}11220\\00001\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}11200\\00001\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}12000\\00001\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}12200\\00001\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}12000\\00011\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}12200\\00012\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}12000\\00012\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}12200\\00010\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}12001\\00011\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}12201\\00012\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}12001\\00012\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}12201\\00010\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}12002\\00011\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}12202\\00012\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}12002\\00012\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}12202\\00010\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}12010\\00001\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}12210\\00001\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}12020\\00001\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}12220\\00001\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}12000\\00101\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}12011\\00111\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}12000\\00102\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}12012\\00112\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}12001\\00101\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}12012\\00111\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}12001\\00102\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}12010\\00112\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}12002\\00101\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}12010\\00111\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}12002\\00102\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}12011\\00112\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}12000\\00111\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}12022\\00122\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}12001\\00111\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}12020\\00122\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}12002\\00111\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}12021\\00122\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}12000\\00120\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}12000\\00122\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}12001\\00120\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}12001\\00122\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}12002\\00120\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}12002\\00122\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}12010\\00100\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}12021\\00110\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}12011\\00100\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}12022\\00110\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}12012\\00100\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}12020\\00110\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}12010\\00121\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}12011\\00121\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}12012\\00121\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}12020\\00101\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}12021\\00101\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}12022\\00101\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}12100\\00001\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}12100\\00010\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}12100\\00011\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}12101\\00010\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}12101\\00011\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}12102\\00010\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}12102\\00011\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}12110\\00001\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}12120\\00001\\\end{smallmatrix}\right)\).

A blocking set showing \(b_3(5,2,2;7,1)\le 745\) is given by: \(\left(\begin{smallmatrix}00100\\00001\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}00110\\00001\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}00101\\00011\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}00102\\00012\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}00102\\00010\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}00120\\00001\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}01000\\00001\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}01100\\00001\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}01000\\00010\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}01100\\00011\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}01000\\00011\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}01100\\00012\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}01000\\00012\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}01100\\00010\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}01001\\00010\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}01101\\00011\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}01001\\00011\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}01101\\00012\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}01001\\00012\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}01101\\00010\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}01002\\00010\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}01102\\00011\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}01002\\00011\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}01102\\00012\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}01002\\00012\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}01102\\00010\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}01010\\00001\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}01110\\00001\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}01020\\00001\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}01120\\00001\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}01000\\00101\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}01022\\00111\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}01001\\00101\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}01020\\00111\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}01002\\00101\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}01021\\00111\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}01000\\00110\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}01012\\00121\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}01000\\00112\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}01010\\00120\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}01001\\00110\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}01010\\00121\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}01001\\00112\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}01011\\00120\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}01002\\00110\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}01011\\00121\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}01002\\00112\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}01012\\00120\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}01000\\00122\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}01001\\00122\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}01002\\00122\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}01010\\00100\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}01010\\00102\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}01011\\00100\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}01011\\00102\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}01012\\00100\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}01012\\00102\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}01010\\00110\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}01020\\00121\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}01011\\00110\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}01021\\00121\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}01012\\00110\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}01022\\00121\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}01020\\00100\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}01021\\00100\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}01022\\00100\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}01210\\00001\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}01202\\00011\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}01201\\00012\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}01200\\00010\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}01200\\00011\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}01202\\00012\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}01201\\00010\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}01201\\00011\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}01200\\00012\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}01202\\00010\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}01220\\00001\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}01200\\00001\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}10002\\00010\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}10002\\00011\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}10002\\00012\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}10000\\00100\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}10000\\00110\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}10000\\00101\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}10000\\00111\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}10001\\00101\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}10001\\00111\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}10000\\00121\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}10000\\00122\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}10001\\00122\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}10010\\00100\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}10011\\00110\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}10010\\00101\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}10011\\00111\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}10011\\00100\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}10012\\00110\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}10011\\00101\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}10012\\00111\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}10011\\00102\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}10012\\00112\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}10012\\00100\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}10010\\00110\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}10012\\00101\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}10010\\00111\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}10012\\00102\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}10010\\00112\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}10011\\00121\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}10011\\00122\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}10011\\00120\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}10012\\00121\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}10012\\00122\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}10010\\00121\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}10010\\00122\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}10010\\00120\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}10020\\00100\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}10022\\00110\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}10020\\00101\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}10022\\00111\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}10020\\00102\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}10022\\00112\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}10021\\00100\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}10020\\00110\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}10021\\00101\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}10020\\00111\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}10021\\00102\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}10020\\00112\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}10022\\00100\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}10021\\00110\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}10022\\00102\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}10021\\00112\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}10022\\00121\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}10022\\00122\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}10022\\00120\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}10020\\00121\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}10020\\00120\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}10021\\00121\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}10021\\00122\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}10021\\00120\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}10100\\00001\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}10110\\00001\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}10100\\00011\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}10101\\00012\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}10101\\00010\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}10120\\00001\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}10200\\00001\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}10220\\00001\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}10200\\00010\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}10201\\00011\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}10200\\00011\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}10202\\00012\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}10200\\00012\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}10201\\00010\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}10202\\00011\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}10201\\00012\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}10202\\00010\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}10210\\00001\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}10002\\01000\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}10002\\01100\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}10002\\01001\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}10002\\01101\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}10002\\01002\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}10002\\01102\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}10000\\01010\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}10000\\01111\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}10000\\01011\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}10000\\01112\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}10000\\01012\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}10000\\01110\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}10001\\01010\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}10001\\01111\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}10001\\01011\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}10001\\01112\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}10001\\01012\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}10001\\01110\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}10002\\01010\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}10002\\01111\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}10002\\01011\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}10002\\01112\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}10002\\01012\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}10002\\01110\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}10000\\01020\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}10000\\01122\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}10000\\01021\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}10000\\01120\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}10000\\01022\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}10000\\01121\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}10001\\01020\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}10001\\01122\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}10001\\01021\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}10001\\01120\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}10001\\01022\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}10001\\01121\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}10002\\01020\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}10002\\01122\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}10002\\01021\\\end{smallmatrix}\right)\), 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\(\left(\begin{smallmatrix}10202\\01210\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}10202\\01211\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}10202\\01212\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}10201\\01221\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}10201\\01222\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}10201\\01220\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}10200\\01221\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}10200\\01222\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}10200\\01220\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}10201\\01202\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}10201\\01200\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}10201\\01201\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}10210\\01210\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}10210\\01211\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}10210\\01212\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}10211\\01210\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}10211\\01211\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}10211\\01212\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}10211\\01221\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}10211\\01222\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}10211\\01220\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}10212\\01202\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}10212\\01200\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}10212\\01201\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}11000\\00001\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}11100\\00001\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}11000\\00012\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}11100\\00010\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}11001\\00012\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}11101\\00010\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}11002\\00012\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}11102\\00010\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}11010\\00001\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}11110\\00001\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}11020\\00001\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}11120\\00001\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}11000\\00101\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}11022\\00111\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}11000\\00102\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}11021\\00112\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}11001\\00101\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}11020\\00111\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}11001\\00102\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}11022\\00112\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}11002\\00101\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}11021\\00111\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}11002\\00102\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}11020\\00112\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}11000\\00110\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}11012\\00121\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}11000\\00111\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}11011\\00122\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}11000\\00112\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}11010\\00120\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}11001\\00110\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}11010\\00121\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}11001\\00111\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}11012\\00122\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}11001\\00112\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}11011\\00120\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}11002\\00110\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}11011\\00121\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}11002\\00111\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}11010\\00122\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}11002\\00112\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}11012\\00120\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}11000\\00120\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}11000\\00122\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}11001\\00120\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}11001\\00122\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}11002\\00120\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}11002\\00122\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}11010\\00100\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}11010\\00101\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}11010\\00102\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}11011\\00100\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}11011\\00101\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}11011\\00102\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}11012\\00100\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}11012\\00101\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}11012\\00102\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}11010\\00110\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}11020\\00121\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}11011\\00110\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}11021\\00121\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}11012\\00110\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}11022\\00121\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}11020\\00100\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}11021\\00100\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}11022\\00100\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}11210\\00001\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}11202\\00011\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}11200\\00011\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}11201\\00011\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}11220\\00001\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}11200\\00001\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}12000\\00001\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}12200\\00001\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}12000\\00012\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}12200\\00010\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}12001\\00012\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}12201\\00010\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}12002\\00012\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}12202\\00010\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}12010\\00001\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}12210\\00001\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}12020\\00001\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}12220\\00001\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}12000\\00100\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}12010\\00110\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}12000\\00101\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}12011\\00111\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}12001\\00100\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}12011\\00110\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}12001\\00101\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}12012\\00111\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}12002\\00100\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}12012\\00110\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}12002\\00101\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}12010\\00111\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}12000\\00110\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}12021\\00121\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}12000\\00111\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}12022\\00122\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}12000\\00112\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}12020\\00120\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}12001\\00110\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}12022\\00121\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}12001\\00111\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}12020\\00122\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}12001\\00112\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}12021\\00120\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}12002\\00110\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}12020\\00121\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}12002\\00111\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}12021\\00122\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}12002\\00112\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}12022\\00120\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}12000\\00121\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}12000\\00122\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}12001\\00121\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}12001\\00122\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}12002\\00121\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}12002\\00122\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}12010\\00102\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}12020\\00112\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}12011\\00102\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}12021\\00112\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}12012\\00102\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}12022\\00112\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}12010\\00120\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}12011\\00120\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}12012\\00120\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}12020\\00100\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}12020\\00101\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}12020\\00102\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}12021\\00100\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}12021\\00101\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}12021\\00102\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}12022\\00100\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}12022\\00101\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}12022\\00102\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}12100\\00001\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}12100\\00011\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}12101\\00011\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}12102\\00011\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}12110\\00001\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}12120\\00001\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}00010\\00001\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}10000\\00001\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}10010\\00001\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}10020\\00001\\\end{smallmatrix}\right)\).

A blocking set showing \(b_3(5,2,2;8,1)\le 844\) is given by: \(\left(\begin{smallmatrix}00100\\00001\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}00110\\00001\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}00100\\00010\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}00102\\00011\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}00100\\00012\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}00101\\00011\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}00102\\00012\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}00102\\00010\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}00120\\00001\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}01000\\00001\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}01100\\00001\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}01000\\00011\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}01100\\00012\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}01000\\00012\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}01100\\00010\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}01001\\00011\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}01101\\00012\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}01001\\00012\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}01101\\00010\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}01002\\00011\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}01102\\00012\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}01002\\00012\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}01102\\00010\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}01000\\00101\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}01022\\00111\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}01000\\00102\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}01021\\00112\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}01001\\00101\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}01020\\00111\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}01001\\00102\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}01022\\00112\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}01002\\00101\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}01021\\00111\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}01002\\00102\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}01020\\00112\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}01000\\00110\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}01012\\00121\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}01000\\00111\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}01011\\00122\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}01001\\00110\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}01010\\00121\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}01001\\00111\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}01012\\00122\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}01002\\00110\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}01011\\00121\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}01002\\00111\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}01010\\00122\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}01000\\00120\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}01000\\00122\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}01001\\00120\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}01001\\00122\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}01002\\00120\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}01002\\00122\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}01010\\00100\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}01010\\00101\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}01011\\00100\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}01011\\00101\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}01012\\00100\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}01012\\00101\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}01010\\00110\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}01020\\00121\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}01010\\00111\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}01022\\00122\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}01010\\00112\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}01021\\00120\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}01011\\00110\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}01021\\00121\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}01011\\00111\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}01020\\00122\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}01011\\00112\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}01022\\00120\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}01012\\00110\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}01022\\00121\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}01012\\00111\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}01021\\00122\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}01012\\00112\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}01020\\00120\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}01020\\00100\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}01020\\00101\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}01020\\00102\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}01021\\00100\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}01021\\00101\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}01021\\00102\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}01022\\00100\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}01022\\00101\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}01022\\00102\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}01210\\00001\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}01202\\00011\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}01200\\00010\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}01200\\00011\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}01201\\00010\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}01201\\00011\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}01202\\00010\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}10000\\00010\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}10000\\00011\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}10000\\00012\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}10001\\00010\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}10001\\00011\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}10001\\00012\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}10002\\00010\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}10002\\00011\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}10002\\00012\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}10000\\00100\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}10000\\00110\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}10000\\00101\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}10000\\00111\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}10001\\00100\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}10001\\00110\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}10001\\00102\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}10001\\00112\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}10002\\00100\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}10002\\00110\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}10002\\00101\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}10002\\00111\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}10002\\00102\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}10002\\00112\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}10000\\00121\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}10000\\00122\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}10001\\00121\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}10001\\00120\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}10002\\00121\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}10002\\00122\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}10002\\00120\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}10011\\00100\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}10012\\00110\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}10011\\00101\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}10012\\00111\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}10012\\00100\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}10010\\00110\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}10012\\00101\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}10010\\00111\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}10012\\00102\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}10010\\00112\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}10011\\00121\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}10011\\00122\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}10011\\00120\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}10010\\00121\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}10010\\00122\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}10020\\00100\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}10022\\00110\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}10020\\00102\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}10022\\00112\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}10021\\00101\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}10020\\00111\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}10022\\00101\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}10021\\00111\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}10022\\00102\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}10021\\00112\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}10022\\00122\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}10020\\00122\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}10020\\00120\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}10021\\00121\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}10021\\00120\\\end{smallmatrix}\right)\), 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\(\left(\begin{smallmatrix}10221\\01120\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}10201\\01022\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}10221\\01121\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}10202\\01020\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}10222\\01122\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}10202\\01021\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}10222\\01120\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}10202\\01022\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}10222\\01121\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}10210\\01000\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}10201\\01100\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}10210\\01001\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}10201\\01101\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}10210\\01002\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}10201\\01102\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}10212\\01000\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}10200\\01100\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}10212\\01001\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}10200\\01101\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}10212\\01002\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}10200\\01102\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}10210\\01010\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}10201\\01111\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}10210\\01011\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}10201\\01112\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}10210\\01012\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}10201\\01110\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}10212\\01010\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}10200\\01111\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}10212\\01011\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}10200\\01112\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}10212\\01012\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}10200\\01110\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}10211\\01020\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}10202\\01122\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}10211\\01021\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}10202\\01120\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}10211\\01022\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}10202\\01121\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}10212\\01020\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}10200\\01122\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}10212\\01021\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}10200\\01120\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}10212\\01022\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}10200\\01121\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}10220\\01000\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}10212\\01100\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}10220\\01001\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}10212\\01101\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}10220\\01002\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}10212\\01102\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}10221\\01000\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}10210\\01100\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}10221\\01001\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}10210\\01101\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}10221\\01002\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}10210\\01102\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}10222\\01000\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}10211\\01100\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}10222\\01001\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}10211\\01101\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}10222\\01002\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}10211\\01102\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}10221\\01010\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}10210\\01111\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}10221\\01011\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}10210\\01112\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}10221\\01012\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}10210\\01110\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}10222\\01010\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}10211\\01111\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}10222\\01011\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}10211\\01112\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}10222\\01012\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}10211\\01110\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}10221\\01020\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}10210\\01122\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}10221\\01021\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}10210\\01120\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}10221\\01022\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}10210\\01121\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}10222\\01020\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}10211\\01122\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}10222\\01021\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}10211\\01120\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}10222\\01022\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}10211\\01121\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}10220\\01210\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}10220\\01211\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}10220\\01212\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}10221\\01210\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}10221\\01211\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}10221\\01212\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}10220\\01221\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}10220\\01222\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}10220\\01220\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}10221\\01221\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}10221\\01222\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}10221\\01220\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}10220\\01202\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}10220\\01200\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}10220\\01201\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}10222\\01202\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}10222\\01200\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}10222\\01201\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}10201\\01210\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}10201\\01211\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}10201\\01212\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}10202\\01210\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}10202\\01211\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}10202\\01212\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}10200\\01210\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}10200\\01211\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}10200\\01212\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}10201\\01221\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}10201\\01222\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}10201\\01220\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}10202\\01221\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}10202\\01222\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}10202\\01220\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}10201\\01202\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}10201\\01200\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}10201\\01201\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}10202\\01202\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}10202\\01200\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}10202\\01201\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}10212\\01210\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}10212\\01211\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}10212\\01212\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}10210\\01210\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}10210\\01211\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}10210\\01212\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}10212\\01221\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}10212\\01222\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}10212\\01220\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}10211\\01221\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}10211\\01222\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}10211\\01220\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}10210\\01202\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}10210\\01200\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}10210\\01201\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}10211\\01202\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}10211\\01200\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}10211\\01201\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}11000\\00010\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}11100\\00011\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}11000\\00011\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}11100\\00012\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}11001\\00010\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}11101\\00011\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}11001\\00011\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}11101\\00012\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}11002\\00010\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}11102\\00011\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}11002\\00011\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}11102\\00012\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}11010\\00001\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}11110\\00001\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}11000\\00100\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}11020\\00110\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}11000\\00101\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}11022\\00111\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}11000\\00102\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}11021\\00112\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}11001\\00100\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}11021\\00110\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}11001\\00101\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}11020\\00111\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}11001\\00102\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}11022\\00112\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}11002\\00100\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}11022\\00110\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}11002\\00101\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}11021\\00111\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}11002\\00102\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}11020\\00112\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}11000\\00110\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}11012\\00121\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}11000\\00112\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}11010\\00120\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}11001\\00110\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}11010\\00121\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}11001\\00112\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}11011\\00120\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}11002\\00110\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}11011\\00121\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}11002\\00112\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}11012\\00120\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}11000\\00120\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}11000\\00121\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}11000\\00122\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}11001\\00120\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}11001\\00121\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}11001\\00122\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}11002\\00120\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}11002\\00121\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}11002\\00122\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}11010\\00100\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}11010\\00102\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}11011\\00100\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}11011\\00102\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}11012\\00100\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}11012\\00102\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}11010\\00111\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}11022\\00122\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}11010\\00112\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}11021\\00120\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}11011\\00111\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}11020\\00122\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}11011\\00112\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}11022\\00120\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}11012\\00111\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}11021\\00122\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}11012\\00112\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}11020\\00120\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}11020\\00101\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}11020\\00102\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}11021\\00101\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}11021\\00102\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}11022\\00101\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}11022\\00102\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}11201\\00012\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}11200\\00010\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}11202\\00012\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}11201\\00010\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}11200\\00012\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}11202\\00010\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}11220\\00001\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}12000\\00001\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}12200\\00001\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}12000\\00011\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}12200\\00012\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}12000\\00012\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}12200\\00010\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}12001\\00011\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}12201\\00012\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}12001\\00012\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}12201\\00010\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}12002\\00011\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}12202\\00012\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}12002\\00012\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}12202\\00010\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}12010\\00001\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}12210\\00001\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}12020\\00001\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}12220\\00001\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}12000\\00101\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}12011\\00111\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}12000\\00102\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}12012\\00112\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}12001\\00101\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}12012\\00111\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}12001\\00102\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}12010\\00112\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}12002\\00101\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}12010\\00111\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}12002\\00102\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}12011\\00112\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}12000\\00110\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}12021\\00121\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}12000\\00111\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}12022\\00122\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}12001\\00110\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}12022\\00121\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}12001\\00111\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}12020\\00122\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}12002\\00110\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}12020\\00121\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}12002\\00111\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}12021\\00122\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}12000\\00120\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}12000\\00122\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}12001\\00120\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}12001\\00122\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}12002\\00120\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}12002\\00122\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}12010\\00100\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}12021\\00110\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}12010\\00102\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}12020\\00112\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}12011\\00100\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}12022\\00110\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}12011\\00102\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}12021\\00112\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}12012\\00100\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}12020\\00110\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}12012\\00102\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}12022\\00112\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}12010\\00120\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}12010\\00121\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}12011\\00120\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}12011\\00121\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}12012\\00120\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}12012\\00121\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}12020\\00100\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}12020\\00101\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}12021\\00100\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}12021\\00101\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}12022\\00100\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}12022\\00101\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}12100\\00001\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}12100\\00010\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}12100\\00011\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}12101\\00010\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}12101\\00011\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}12102\\00010\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}12102\\00011\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}12110\\00001\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}12120\\00001\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}00010\\00001\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}10000\\00001\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}10010\\00001\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}10020\\00001\\\end{smallmatrix}\right)\).

A blocking set showing \(b_3(5,2,2;9,1)\le 935\) is given by: \(\left(\begin{smallmatrix}00010\\00001\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}01110\\00001\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}00100\\00001\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}01101\\00010\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}00100\\00010\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}00100\\00011\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}01100\\00010\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}00100\\00012\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}01102\\00010\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}00101\\00010\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}01100\\00001\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}00101\\00011\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}01101\\00012\\\end{smallmatrix}\right)\), 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\(\left(\begin{smallmatrix}11011\\00121\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}10200\\01202\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}12001\\00121\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}10200\\01020\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}10120\\01220\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}10120\\01221\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}10120\\01222\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}10121\\01220\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}11010\\00122\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}10121\\01221\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}10122\\01220\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}12002\\00122\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}10122\\01221\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}10202\\01022\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}10122\\01222\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}10200\\01001\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}10200\\01002\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}10201\\01000\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}11021\\00100\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}10201\\01001\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}10201\\01002\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}10210\\01211\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}10202\\01001\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}10210\\01011\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}10212\\01212\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}12000\\00101\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}10212\\01010\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}10211\\01210\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}12001\\00102\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}11020\\00100\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}12001\\00100\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}10210\\01010\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}10210\\01012\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}10211\\01011\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}12002\\00101\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}11021\\00102\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}10210\\01210\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}12000\\00102\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}11022\\00100\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}10211\\01211\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}12000\\00100\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}11021\\00101\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}10210\\01212\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}10220\\01020\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}10220\\01021\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}10220\\01022\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}10221\\01021\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}10221\\01022\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}10212\\01210\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}10222\\01022\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}10200\\01100\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}10200\\01101\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}10201\\01100\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}11011\\00110\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}10201\\01102\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}10200\\01221\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}10202\\01100\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}12012\\00110\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}10202\\01101\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}10202\\01102\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}10200\\01110\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}10200\\01112\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}10201\\01110\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}11010\\00111\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}10201\\01111\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}10201\\01112\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}10202\\01222\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}10202\\01110\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}12010\\00111\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}10200\\01120\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}10200\\01121\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}10200\\01122\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}10201\\01122\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}10201\\01220\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}10202\\01120\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}12011\\00112\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}10202\\01121\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}10202\\01122\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}10210\\01101\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}10210\\01102\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}10211\\01101\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}10211\\01102\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}10202\\01221\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}10212\\01100\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}12011\\00110\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}10212\\01101\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}10212\\01102\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}10210\\01111\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}10210\\01112\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}10211\\01110\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}11012\\00111\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}10211\\01111\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}10211\\01112\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}10201\\01222\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}10212\\01110\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}12012\\00111\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}10212\\01111\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}10212\\01112\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}10210\\01121\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}10211\\01120\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}11011\\00112\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}10211\\01122\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}10200\\01220\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}10212\\01120\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}12010\\00112\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}10212\\01121\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}10212\\01122\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}10220\\01100\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}10221\\01100\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}11012\\00110\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}10221\\01102\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}10201\\01221\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}10222\\01100\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}12010\\00110\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}10222\\01101\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}10222\\01102\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}10220\\01111\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}10220\\01112\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}10221\\01111\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}10221\\01112\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}10200\\01222\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}10222\\01110\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}12011\\00111\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}10222\\01112\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}10220\\01120\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}10220\\01122\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}10221\\01120\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}11010\\00112\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}10221\\01121\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}10221\\01122\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}10202\\01220\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}10222\\01120\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}12012\\00112\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}10222\\01122\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}11001\\00120\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}10220\\01201\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}10222\\01202\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}12020\\00121\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}11002\\00122\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}10221\\01200\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}12021\\00122\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}11000\\00120\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}10222\\01201\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}12021\\00120\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}11002\\00121\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}12022\\00121\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}11001\\00122\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}10220\\01200\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}12020\\00122\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}10220\\01202\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}11002\\00120\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}10222\\01200\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}12020\\00120\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}11001\\00121\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}11000\\00122\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}12022\\00122\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}11000\\00010\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}11000\\00011\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}11000\\00012\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}11001\\00011\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}11002\\00010\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}12120\\00001\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}11002\\00011\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}11002\\00012\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}11020\\00001\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}12102\\00010\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}12101\\00012\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}12101\\00010\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}12102\\00011\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}12100\\00012\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}12100\\00010\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}12101\\00011\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}12102\\00012\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}12110\\00001\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}11200\\00001\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}11200\\00010\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}11200\\00012\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}11201\\00010\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}11201\\00011\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}11201\\00012\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}11202\\00010\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}12100\\00001\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}11202\\00011\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}11202\\00012\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}11210\\00001\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}11220\\00001\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}12000\\00010\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}12000\\00011\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}12000\\00012\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}12001\\00010\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}12001\\00011\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}12001\\00012\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}12002\\00011\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}12010\\00001\\\end{smallmatrix}\right)\).

A blocking set showing \(b_3(5,2,2;10,1)\le 1020\) is given by: \(\left(\begin{smallmatrix}00010\\00001\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}01110\\00001\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}00100\\00001\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}01101\\00010\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}00100\\00010\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}00100\\00011\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}01100\\00010\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}00101\\00011\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}01101\\00012\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}00101\\00012\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}01101\\00011\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}00102\\00010\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}01120\\00001\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}00102\\00011\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}01102\\00011\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}00102\\00012\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}01100\\00012\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}00110\\00001\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}01100\\00011\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}01000\\00001\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}01011\\00100\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}01000\\00010\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}01000\\00012\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}01012\\00100\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}01001\\00010\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}01010\\00001\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}01001\\00012\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}01011\\00101\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}01002\\00010\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}01210\\00001\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}01002\\00012\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}01010\\00102\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}01010\\00101\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}01020\\00001\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}01012\\00102\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}01000\\00100\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}01000\\00101\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}01001\\00100\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}01000\\00102\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}01021\\00100\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}01001\\00101\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}01011\\00120\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}01002\\00100\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}01201\\00010\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}01002\\00102\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}01001\\00120\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}01000\\00110\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}01000\\00111\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}01001\\00111\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}01011\\00122\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}01001\\00112\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}01011\\00111\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}01002\\00110\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}01200\\00011\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}01002\\00111\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}01022\\00111\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}01002\\00112\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}01000\\00122\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}01000\\00121\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}01020\\00100\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}01001\\00121\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}01011\\00121\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}01001\\00122\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}01011\\00112\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}01002\\00121\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}01020\\00112\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}01002\\00122\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}01020\\00101\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}01010\\00121\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}01202\\00010\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}01010\\00110\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}01010\\00112\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}01021\\00101\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}01010\\00120\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}01012\\00110\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}01201\\00011\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}01012\\00111\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}01021\\00112\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}01010\\00122\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}01022\\00101\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}01012\\00120\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}01200\\00012\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}01012\\00121\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}01022\\00110\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}01012\\00122\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}01020\\00102\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}01022\\00102\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}01022\\00112\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}01020\\00110\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}01021\\00111\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}01202\\00011\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}01020\\00120\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}01020\\00121\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}01021\\00120\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}01021\\00121\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}01021\\00122\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}01022\\00120\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}01201\\00012\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}01022\\00121\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}01200\\00001\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}10000\\00001\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}10000\\01111\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}10000\\00010\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}10000\\00011\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}10000\\01110\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}10000\\00012\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}10000\\01112\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}10001\\00011\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}10001\\01110\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}10001\\00012\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}10002\\01112\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}10002\\00011\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}10002\\01110\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}10002\\00012\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}10001\\01112\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}10010\\00001\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}10002\\01111\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}10020\\00001\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}10001\\01111\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}10000\\00100\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}10000\\00101\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}10000\\01101\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}10000\\00102\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}10000\\01121\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}10001\\00100\\\end{smallmatrix}\right)\), 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\(\left(\begin{smallmatrix}10210\\01210\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}12000\\00102\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}11022\\00100\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}12000\\00100\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}11021\\00101\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}10210\\01212\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}12001\\00101\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}10220\\01020\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}10220\\01021\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}10220\\01022\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}10221\\01021\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}10222\\01020\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}12002\\00102\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}10222\\01021\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}10222\\01022\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}10200\\01100\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}10200\\01101\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}10200\\01102\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}10201\\01100\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}11011\\00110\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}10201\\01101\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}10201\\01102\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}10200\\01221\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}10202\\01102\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}10200\\01110\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}10200\\01111\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}10200\\01112\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}10201\\01111\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}10202\\01110\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}12010\\00111\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}10202\\01111\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}10202\\01112\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}10200\\01120\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}10200\\01121\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}10200\\01122\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}10201\\01120\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}11012\\00112\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}10201\\01122\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}10201\\01220\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}10202\\01120\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}12011\\00112\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}10202\\01121\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}10210\\01100\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}10210\\01101\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}10210\\01102\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}10211\\01100\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}11010\\00110\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}10211\\01101\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}10212\\01100\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}12011\\00110\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}10212\\01101\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}10212\\01102\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}10210\\01110\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}10210\\01111\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}10210\\01112\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}10211\\01110\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}11012\\00111\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}10211\\01112\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}10201\\01222\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}10212\\01110\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}12012\\00111\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}10212\\01111\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}10212\\01112\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}10210\\01120\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}10210\\01121\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}10210\\01122\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}10211\\01120\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}11011\\00112\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}10211\\01121\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}10211\\01122\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}10200\\01220\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}10212\\01120\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}12010\\00112\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}10212\\01121\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}10212\\01122\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}10220\\01100\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}10220\\01101\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}10220\\01102\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}10221\\01100\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}11012\\00110\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}10221\\01101\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}10221\\01102\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}10201\\01221\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}10222\\01102\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}10220\\01110\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}10220\\01111\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}10221\\01110\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}11011\\00111\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}10221\\01111\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}10221\\01112\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}10200\\01222\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}10222\\01110\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}12011\\00111\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}10222\\01112\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}10220\\01120\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}10220\\01121\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}10221\\01121\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}10221\\01122\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}10202\\01220\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}10222\\01121\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}10222\\01122\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}10220\\01201\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}12022\\00120\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}11000\\00121\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}10222\\01202\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}12020\\00121\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}11002\\00122\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}10221\\01200\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}12021\\00122\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}11000\\00120\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}10222\\01201\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}12021\\00120\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}11002\\00121\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}10221\\01202\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}10220\\01200\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}12020\\00122\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}10220\\01202\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}11002\\00120\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}10221\\01201\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}10222\\01200\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}12020\\00120\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}11001\\00121\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}12021\\00121\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}11000\\00122\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}12022\\00122\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}11000\\00001\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}11000\\00010\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}11000\\00011\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}11000\\00012\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}11001\\00010\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}11010\\00001\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}11001\\00012\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}11002\\00010\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}12120\\00001\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}11002\\00011\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}11020\\00001\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}12102\\00010\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}12100\\00011\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}12101\\00012\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}12101\\00010\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}12102\\00011\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}12100\\00012\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}12100\\00010\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}12101\\00011\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}12102\\00012\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}11200\\00001\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}11200\\00010\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}11200\\00011\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}11200\\00012\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}11201\\00010\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}11201\\00011\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}11201\\00012\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}11202\\00010\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}12100\\00001\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}11202\\00011\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}11202\\00012\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}11210\\00001\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}12000\\00001\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}12000\\00010\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}12000\\00011\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}12000\\00012\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}12001\\00010\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}12001\\00011\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}12002\\00010\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}12020\\00001\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}12002\\00012\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}12010\\00001\\\end{smallmatrix}\right)\).

A blocking set showing \(b_3(5,2,2;11,1)\le 1105\) is given by: \(\left(\begin{smallmatrix}00010\\00001\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}01110\\00001\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}00100\\00001\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}01101\\00010\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}00100\\00010\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}00100\\00011\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}01100\\00010\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}00100\\00012\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}01102\\00010\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}00101\\00010\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}01100\\00001\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}00101\\00011\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}01101\\00012\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}00102\\00010\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}01120\\00001\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}00102\\00011\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}01102\\00011\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}00102\\00012\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}01100\\00012\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}00110\\00001\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}01100\\00011\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}01000\\00001\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}01011\\00100\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}01000\\00010\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}01000\\00011\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}01010\\00100\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}01000\\00012\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}01012\\00100\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}01001\\00010\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}01010\\00001\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}01001\\00011\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}01011\\00102\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}01001\\00012\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}01011\\00101\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}01002\\00010\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}01210\\00001\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}01002\\00011\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}01012\\00101\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}01002\\00012\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}01010\\00102\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}01010\\00101\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}01020\\00001\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}01012\\00102\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}01000\\00100\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}01000\\00101\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}01001\\00100\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}01000\\00102\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}01021\\00100\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}01001\\00101\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}01011\\00120\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}01001\\00102\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}01011\\00110\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}01002\\00100\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}01201\\00010\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}01002\\00101\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}01021\\00110\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}01002\\00102\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}01001\\00120\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}01000\\00110\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}01000\\00111\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}01001\\00110\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}01001\\00111\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}01011\\00122\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}01002\\00110\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}01200\\00011\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}01002\\00111\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}01022\\00111\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}01002\\00112\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}01000\\00122\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}01000\\00120\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}01000\\00121\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}01020\\00100\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}01001\\00121\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}01011\\00121\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}01001\\00122\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}01011\\00112\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}01002\\00121\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}01020\\00112\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}01002\\00122\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}01020\\00101\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}01010\\00121\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}01010\\00111\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}01202\\00010\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}01020\\00111\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}01010\\00110\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}01010\\00112\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}01021\\00101\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}01012\\00110\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}01201\\00011\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}01012\\00111\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}01021\\00112\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}01010\\00122\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}01022\\00101\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}01012\\00120\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}01200\\00012\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}01012\\00121\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}01022\\00110\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}01012\\00122\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}01020\\00102\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}01022\\00102\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}01022\\00112\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}01020\\00110\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}01021\\00111\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}01202\\00011\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}01020\\00120\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}01020\\00121\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}01021\\00120\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}01021\\00121\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}01021\\00122\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}01022\\00120\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}01201\\00012\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}01022\\00121\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}01022\\00122\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}01220\\00001\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}01200\\00001\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}10000\\00001\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}10000\\01111\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}10000\\00010\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}10000\\00011\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}10000\\01110\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}10000\\00012\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}10000\\01112\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}10001\\00010\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}11110\\00001\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}10001\\00011\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}10001\\01110\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}10001\\00012\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}10002\\01112\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}10002\\00010\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}12220\\00001\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}10002\\00011\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}10002\\01110\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}10002\\00012\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}10001\\01112\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}10000\\00100\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}10000\\00101\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}10000\\01101\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}10000\\00102\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}10000\\01121\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}10001\\00100\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}11101\\00010\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}10001\\00101\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}10010\\01101\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}10001\\00102\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}10020\\01121\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}10002\\00100\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}12202\\00010\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}10002\\00101\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}10020\\01101\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}10002\\00102\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}10010\\01121\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}10000\\00110\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}10000\\00111\\\end{smallmatrix}\right)\), 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\(\left(\begin{smallmatrix}10121\\01222\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}10202\\01200\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}10122\\01220\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}12002\\00122\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}10122\\01221\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}10202\\01022\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}10122\\01222\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}10200\\01000\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}10200\\01002\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}10201\\01000\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}11021\\00100\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}10201\\01001\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}10201\\01002\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}10210\\01211\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}10202\\01000\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}12002\\00100\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}10202\\01001\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}10210\\01011\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}10202\\01002\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}11020\\00101\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}10212\\01212\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}12000\\00101\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}10212\\01010\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}11022\\00102\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}10211\\01210\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}12001\\00102\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}10211\\01012\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}11020\\00100\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}10212\\01211\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}12001\\00100\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}10212\\01011\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}10210\\01010\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}10210\\01012\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}10211\\01010\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}11022\\00101\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}10211\\01011\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}10211\\01212\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}12002\\00101\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}11021\\00102\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}10210\\01210\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}12000\\00102\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}11022\\00100\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}11021\\00101\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}10210\\01212\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}12001\\00101\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}10220\\01020\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}10220\\01021\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}10220\\01022\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}10221\\01020\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}11020\\00102\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}10221\\01021\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}10221\\01022\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}10212\\01210\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}10222\\01020\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}12002\\00102\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}10222\\01022\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}10200\\01100\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}10200\\01101\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}10200\\01102\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}10201\\01100\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}11011\\00110\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}10201\\01101\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}10201\\01102\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}10200\\01221\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}10202\\01102\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}10200\\01110\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}10200\\01111\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}10200\\01112\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}10201\\01111\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}10202\\01110\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}12010\\00111\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}10202\\01111\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}10202\\01112\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}10200\\01120\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}10200\\01121\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}10200\\01122\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}10201\\01120\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}11012\\00112\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}10201\\01121\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}10201\\01122\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}10201\\01220\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}10202\\01120\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}12011\\00112\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}10202\\01121\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}10202\\01122\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}10210\\01100\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}10210\\01101\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}10211\\01100\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}11010\\00110\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}10211\\01101\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}10211\\01102\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}10202\\01221\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}10212\\01100\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}12011\\00110\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}10212\\01101\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}10212\\01102\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}10210\\01110\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}10210\\01111\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}10210\\01112\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}10211\\01110\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}11012\\00111\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}10211\\01111\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}10211\\01112\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}10201\\01222\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}10212\\01110\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}12012\\00111\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}10212\\01111\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}10212\\01112\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}10210\\01120\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}10210\\01121\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}10210\\01122\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}10211\\01120\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}11011\\00112\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}10211\\01121\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}10211\\01122\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}10200\\01220\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}10212\\01120\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}12010\\00112\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}10212\\01121\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}10212\\01122\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}10220\\01100\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}10220\\01101\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}10220\\01102\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}10221\\01100\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}11012\\00110\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}10221\\01101\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}10221\\01102\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}10201\\01221\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}10222\\01100\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}12010\\00110\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}10222\\01101\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}10222\\01102\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}10220\\01112\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}10221\\01110\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}11011\\00111\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}10221\\01111\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}10221\\01112\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}10200\\01222\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}10222\\01110\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}12011\\00111\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}10222\\01111\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}10222\\01112\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}10220\\01120\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}10220\\01121\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}10220\\01122\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}10221\\01120\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}11010\\00112\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}10221\\01121\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}10221\\01122\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}10202\\01220\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}10222\\01120\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}12012\\00112\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}10222\\01121\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}10222\\01122\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}10220\\01201\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}12022\\00120\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}11000\\00121\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}10222\\01202\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}12020\\00121\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}11002\\00122\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}10221\\01200\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}12021\\00122\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}11000\\00120\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}10222\\01201\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}12021\\00120\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}11002\\00121\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}10221\\01202\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}12022\\00121\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}11001\\00122\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}10220\\01200\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}12020\\00122\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}10220\\01202\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}11002\\00120\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}10221\\01201\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}10222\\01200\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}12020\\00120\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}11001\\00121\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}12021\\00121\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}11000\\00122\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}12022\\00122\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}11000\\00001\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}11000\\00010\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}11000\\00011\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}11000\\00012\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}11001\\00010\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}11010\\00001\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}11001\\00012\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}11002\\00010\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}12120\\00001\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}11002\\00011\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}11020\\00001\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}12102\\00010\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}12100\\00011\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}12101\\00012\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}12101\\00010\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}12102\\00011\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}12100\\00012\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}12100\\00010\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}12101\\00011\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}12102\\00012\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}12110\\00001\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}11200\\00001\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}11200\\00010\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}11200\\00011\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}11200\\00012\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}11201\\00010\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}11201\\00011\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}11201\\00012\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}11202\\00010\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}12100\\00001\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}11202\\00011\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}11202\\00012\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}11210\\00001\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}11220\\00001\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}12000\\00001\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}12000\\00010\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}12000\\00011\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}12000\\00012\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}12001\\00010\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}12001\\00011\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}12002\\00010\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}12020\\00001\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}12002\\00012\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}12010\\00001\\\end{smallmatrix}\right)\).

A blocking set with line multiplicity \(4\) showing \(b_3(5,2,2;7)\le 690\) is given by: \(\left(\begin{smallmatrix}00100\\00010\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}00102\\00011\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}00100\\00011\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}00101\\00012\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}00100\\00012\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}00101\\00010\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}00101\\00011\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}00102\\00012\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}00102\\00010\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}01010\\00001\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}01010\\00001\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}01010\\00001\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}01010\\00001\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}01110\\00001\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}01110\\00001\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}01110\\00001\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}01110\\00001\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}01000\\00100\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}01020\\00110\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}01000\\00101\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}01022\\00111\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}01000\\00102\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}01021\\00112\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}01001\\00100\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}01021\\00110\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}01001\\00101\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}01020\\00111\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}01001\\00102\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}01022\\00112\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}01002\\00100\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}01022\\00110\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}01002\\00101\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}01021\\00111\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}01002\\00102\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}01020\\00112\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}01000\\00120\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}01000\\00121\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}01000\\00122\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}01001\\00120\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}01001\\00121\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}01001\\00122\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}01002\\00120\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}01002\\00121\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}01002\\00122\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}01010\\00110\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}01020\\00121\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}01010\\00111\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}01022\\00122\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}01010\\00112\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}01021\\00120\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}01011\\00110\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}01021\\00121\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}01011\\00111\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}01020\\00122\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}01011\\00112\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}01022\\00120\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}01012\\00110\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}01022\\00121\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}01012\\00111\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}01021\\00122\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}01012\\00112\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}01020\\00120\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}01020\\00100\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}01020\\00101\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}01020\\00102\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}01021\\00100\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}01021\\00101\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}01021\\00102\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}01022\\00100\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}01022\\00101\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}01022\\00102\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}01220\\00001\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}01220\\00001\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}01220\\00001\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}01220\\00001\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}10000\\00010\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}10000\\00011\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}10000\\00012\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}10001\\00010\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}10001\\00011\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}10001\\00012\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}10002\\00010\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}10002\\00011\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}10002\\00012\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}10100\\00001\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}10100\\00001\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}10100\\00001\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}10100\\00001\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}10110\\00001\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}10110\\00001\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}10110\\00001\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}10110\\00001\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}10100\\00010\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}10100\\00010\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}10100\\00010\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}10100\\00010\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}10102\\00011\\\end{smallmatrix}\right)\), 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\(\left(\begin{smallmatrix}10212\\01012\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}10212\\01012\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}10212\\01012\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}10212\\01012\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}10200\\01110\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}10200\\01110\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}10200\\01110\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}10200\\01110\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}10210\\01020\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}10201\\01122\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}10210\\01021\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}10201\\01120\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}10210\\01022\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}10201\\01121\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}10211\\01020\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}10202\\01122\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}10211\\01021\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}10202\\01120\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}10211\\01022\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}10202\\01121\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}10212\\01020\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}10200\\01122\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}10212\\01021\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}10200\\01120\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}10212\\01022\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}10200\\01121\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}10220\\01210\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}10220\\01211\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}10220\\01212\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}10221\\01210\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}10221\\01211\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}10221\\01212\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}10222\\01210\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}10222\\01211\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}10222\\01212\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}10220\\01221\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}10220\\01221\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}10220\\01221\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}10220\\01221\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}10220\\01222\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}10220\\01222\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}10220\\01222\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}10220\\01222\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}10220\\01220\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}10220\\01220\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}10220\\01220\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}10220\\01220\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}10221\\01221\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}10221\\01221\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}10221\\01221\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}10221\\01221\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}10221\\01222\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}10221\\01222\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}10221\\01222\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}10221\\01222\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}10221\\01220\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}10221\\01220\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}10221\\01220\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}10221\\01220\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}10222\\01221\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}10222\\01221\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}10222\\01221\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}10222\\01221\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}10222\\01222\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}10222\\01222\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}10222\\01222\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}10222\\01222\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}10222\\01220\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}10222\\01220\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}10222\\01220\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}10222\\01220\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}10220\\01202\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}10220\\01200\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}10220\\01201\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}10221\\01202\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}10221\\01200\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}10221\\01201\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}10222\\01202\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}10222\\01200\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}10222\\01201\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}11010\\00001\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}11010\\00001\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}11010\\00001\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}11010\\00001\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}11110\\00001\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}11110\\00001\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}11110\\00001\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}11110\\00001\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}11000\\00100\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}11020\\00110\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}11000\\00101\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}11022\\00111\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}11000\\00102\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}11021\\00112\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}11001\\00100\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}11021\\00110\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}11001\\00101\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}11020\\00111\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}11001\\00102\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}11022\\00112\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}11002\\00100\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}11022\\00110\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}11002\\00101\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}11021\\00111\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}11002\\00102\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}11020\\00112\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}11000\\00120\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}11000\\00121\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}11000\\00122\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}11001\\00120\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}11001\\00121\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}11001\\00122\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}11002\\00120\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}11002\\00121\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}11002\\00122\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}11010\\00110\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}11020\\00121\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}11010\\00111\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}11022\\00122\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}11010\\00112\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}11021\\00120\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}11011\\00110\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}11021\\00121\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}11011\\00111\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}11020\\00122\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}11011\\00112\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}11022\\00120\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}11012\\00110\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}11022\\00121\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}11012\\00111\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}11021\\00122\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}11012\\00112\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}11020\\00120\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}11020\\00100\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}11020\\00101\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}11020\\00102\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}11021\\00100\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}11021\\00101\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}11021\\00102\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}11022\\00100\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}11022\\00101\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}11022\\00102\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}11220\\00001\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}11220\\00001\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}11220\\00001\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}11220\\00001\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}12000\\00001\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}12000\\00001\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}12000\\00001\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}12000\\00001\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}12200\\00001\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}12200\\00001\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}12200\\00001\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}12200\\00001\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}12000\\00110\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}12021\\00121\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}12000\\00111\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}12022\\00122\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}12000\\00112\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}12020\\00120\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}12001\\00110\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}12022\\00121\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}12001\\00111\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}12020\\00122\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}12001\\00112\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}12021\\00120\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}12002\\00110\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}12020\\00121\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}12002\\00111\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}12021\\00122\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}12002\\00112\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}12022\\00120\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}12010\\00100\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}12021\\00110\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}12010\\00101\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}12022\\00111\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}12010\\00102\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}12020\\00112\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}12011\\00100\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}12022\\00110\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}12011\\00101\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}12020\\00111\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}12011\\00102\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}12021\\00112\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}12012\\00100\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}12020\\00110\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}12012\\00101\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}12021\\00111\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}12012\\00102\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}12022\\00112\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}12010\\00120\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}12010\\00121\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}12010\\00122\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}12011\\00120\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}12011\\00121\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}12011\\00122\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}12012\\00120\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}12012\\00121\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}12012\\00122\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}12020\\00100\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}12020\\00101\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}12020\\00102\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}12021\\00100\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}12021\\00101\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}12021\\00102\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}12022\\00100\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}12022\\00101\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}12022\\00102\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}12120\\00001\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}12120\\00001\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}12120\\00001\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}12120\\00001\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}00010\\00001\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}00010\\00001\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}00010\\00001\\\end{smallmatrix}\right)\).

A blocking set with line multiplicity \(4\) showing \(b_3(5,2,2;8)\le 784\) is given by: \(\left(\begin{smallmatrix}00100\\00010\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}00100\\00010\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}00102\\00011\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}00102\\00011\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}00100\\00011\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}00100\\00011\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}00101\\00012\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}00101\\00012\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}00100\\00012\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}00100\\00012\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}00101\\00010\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}00101\\00010\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}00101\\00011\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}00101\\00011\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}00102\\00012\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}00102\\00012\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}00102\\00010\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}00102\\00010\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}01010\\00001\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}01010\\00001\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}01010\\00001\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}01010\\00001\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}01110\\00001\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}01110\\00001\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}01110\\00001\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}01110\\00001\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}01000\\00100\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}01020\\00110\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}01000\\00101\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}01022\\00111\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}01000\\00102\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}01021\\00112\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}01001\\00100\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}01021\\00110\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}01001\\00101\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}01020\\00111\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}01001\\00102\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}01022\\00112\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}01002\\00100\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}01022\\00110\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}01002\\00101\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}01021\\00111\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}01002\\00102\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}01020\\00112\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}01000\\00120\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}01000\\00121\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}01000\\00122\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}01001\\00120\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}01001\\00121\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}01001\\00122\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}01002\\00120\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}01002\\00121\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}01002\\00122\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}01010\\00110\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}01020\\00121\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}01010\\00111\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}01022\\00122\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}01010\\00112\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}01021\\00120\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}01011\\00110\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}01021\\00121\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}01011\\00111\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}01020\\00122\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}01011\\00112\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}01022\\00120\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}01012\\00110\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}01022\\00121\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}01012\\00111\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}01021\\00122\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}01012\\00112\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}01020\\00120\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}01020\\00100\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}01020\\00101\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}01020\\00102\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}01021\\00100\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}01021\\00101\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}01021\\00102\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}01022\\00100\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}01022\\00101\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}01022\\00102\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}01220\\00001\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}01220\\00001\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}01220\\00001\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}01220\\00001\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}10000\\00010\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}10000\\00010\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}10000\\00011\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}10000\\00011\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}10000\\00012\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}10000\\00012\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}10001\\00010\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}10001\\00010\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}10001\\00011\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}10001\\00011\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}10001\\00012\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}10001\\00012\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}10002\\00010\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}10002\\00010\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}10002\\00011\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}10002\\00011\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}10002\\00012\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}10002\\00012\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}10100\\00001\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}10100\\00001\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}10100\\00001\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}10100\\00001\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}10110\\00001\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}10110\\00001\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}10110\\00001\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}10110\\00001\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}10100\\00010\\\end{smallmatrix}\right)\), 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\(\left(\begin{smallmatrix}10220\\01010\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}10212\\01111\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}10212\\01111\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}10212\\01111\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}10212\\01111\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}10220\\01011\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}10220\\01011\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}10220\\01011\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}10220\\01011\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}10212\\01112\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}10212\\01112\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}10212\\01112\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}10212\\01112\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}10220\\01012\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}10220\\01012\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}10220\\01012\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}10220\\01012\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}10212\\01110\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}10212\\01110\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}10212\\01110\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}10212\\01110\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}10221\\01010\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}10221\\01010\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}10221\\01010\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}10221\\01010\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}10210\\01111\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}10210\\01111\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}10210\\01111\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}10210\\01111\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}10221\\01011\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}10221\\01011\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}10221\\01011\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}10221\\01011\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}10210\\01112\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}10210\\01112\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}10210\\01112\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}10210\\01112\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}10221\\01012\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}10221\\01012\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}10221\\01012\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}10221\\01012\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}10210\\01110\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}10210\\01110\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}10210\\01110\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}10210\\01110\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}10222\\01010\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}10222\\01010\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}10222\\01010\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}10222\\01010\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}10211\\01111\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}10211\\01111\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}10211\\01111\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}10211\\01111\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}10222\\01011\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}10222\\01011\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}10222\\01011\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}10222\\01011\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}10211\\01112\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}10211\\01112\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}10211\\01112\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}10211\\01112\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}10222\\01012\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}10222\\01012\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}10222\\01012\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}10222\\01012\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}10211\\01110\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}10211\\01110\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}10211\\01110\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}10211\\01110\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}10220\\01020\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}10212\\01122\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}10220\\01021\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}10212\\01120\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}10220\\01022\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}10212\\01121\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}10221\\01020\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}10210\\01122\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}10221\\01021\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}10210\\01120\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}10221\\01022\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}10210\\01121\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}10222\\01020\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}10211\\01122\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}10222\\01021\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}10211\\01120\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}10222\\01022\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}10211\\01121\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}10220\\01210\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}10220\\01211\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}10220\\01212\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}10221\\01210\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}10221\\01211\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}10221\\01212\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}10222\\01210\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}10222\\01211\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}10222\\01212\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}10220\\01221\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}10220\\01222\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}10220\\01220\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}10221\\01221\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}10221\\01222\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}10221\\01220\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}10222\\01221\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}10222\\01222\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}10222\\01220\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}10201\\01210\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}10201\\01211\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}10201\\01212\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}10202\\01210\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}10202\\01211\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}10202\\01212\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}10200\\01210\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}10200\\01211\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}10200\\01212\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}10201\\01221\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}10201\\01221\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}10201\\01221\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}10201\\01221\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}10201\\01222\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}10201\\01222\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}10201\\01222\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}10201\\01222\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}10201\\01220\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}10201\\01220\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}10201\\01220\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}10201\\01220\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}10202\\01221\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}10202\\01221\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}10202\\01221\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}10202\\01221\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}10202\\01222\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}10202\\01222\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}10202\\01222\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}10202\\01222\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}10202\\01220\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}10202\\01220\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}10202\\01220\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}10202\\01220\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}10200\\01221\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}10200\\01221\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}10200\\01221\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}10200\\01221\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}10200\\01222\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}10200\\01222\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}10200\\01222\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}10200\\01222\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}10200\\01220\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}10200\\01220\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}10200\\01220\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}10200\\01220\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}10201\\01202\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}10201\\01200\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}10201\\01201\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}10202\\01202\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}10202\\01200\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}10202\\01201\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}10200\\01202\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}10200\\01200\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}10200\\01201\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}11020\\00001\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}11020\\00001\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}11020\\00001\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}11020\\00001\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}11120\\00001\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}11120\\00001\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}11120\\00001\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}11120\\00001\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}11000\\00100\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}11020\\00110\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}11000\\00101\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}11022\\00111\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}11000\\00102\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}11021\\00112\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}11001\\00100\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}11021\\00110\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}11001\\00101\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}11020\\00111\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}11001\\00102\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}11022\\00112\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}11002\\00100\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}11022\\00110\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}11002\\00101\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}11021\\00111\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}11002\\00102\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}11020\\00112\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}11000\\00110\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}11012\\00121\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}11000\\00111\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}11011\\00122\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}11000\\00112\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}11010\\00120\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}11001\\00110\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}11010\\00121\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}11001\\00111\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}11012\\00122\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}11001\\00112\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}11011\\00120\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}11002\\00110\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}11011\\00121\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}11002\\00111\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}11010\\00122\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}11002\\00112\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}11012\\00120\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}11000\\00120\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}11000\\00121\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}11000\\00122\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}11001\\00120\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}11001\\00121\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}11001\\00122\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}11002\\00120\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}11002\\00121\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}11002\\00122\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}11010\\00100\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}11010\\00101\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}11010\\00102\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}11011\\00100\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}11011\\00101\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}11011\\00102\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}11012\\00100\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}11012\\00101\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}11012\\00102\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}11200\\00001\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}11200\\00001\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}11200\\00001\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}11200\\00001\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}12010\\00001\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}12010\\00001\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}12010\\00001\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}12010\\00001\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}12210\\00001\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}12210\\00001\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}12210\\00001\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}12210\\00001\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}12000\\00100\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}12010\\00110\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}12000\\00101\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}12011\\00111\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}12000\\00102\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}12012\\00112\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}12001\\00100\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}12011\\00110\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}12001\\00101\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}12012\\00111\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}12001\\00102\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}12010\\00112\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}12002\\00100\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}12012\\00110\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}12002\\00101\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}12010\\00111\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}12002\\00102\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}12011\\00112\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}12000\\00110\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}12021\\00121\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}12000\\00111\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}12022\\00122\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}12000\\00112\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}12020\\00120\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}12001\\00110\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}12022\\00121\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}12001\\00111\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}12020\\00122\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}12001\\00112\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}12021\\00120\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}12002\\00110\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}12020\\00121\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}12002\\00111\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}12021\\00122\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}12002\\00112\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}12022\\00120\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}12000\\00120\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}12000\\00121\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}12000\\00122\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}12001\\00120\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}12001\\00121\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}12001\\00122\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}12002\\00120\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}12002\\00121\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}12002\\00122\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}12020\\00100\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}12020\\00101\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}12020\\00102\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}12021\\00100\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}12021\\00101\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}12021\\00102\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}12022\\00100\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}12022\\00101\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}12022\\00102\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}12100\\00001\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}12100\\00001\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}12100\\00001\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}12100\\00001\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}00010\\00001\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}00010\\00001\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}00010\\00001\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}00010\\00001\\\end{smallmatrix}\right)\).

A blocking set with line multiplicity \(9\) showing \(b_3(5,2,2;11)\le 1050\) is given by: \(\left(\begin{smallmatrix}00100\\00001\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}00110\\00001\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}00100\\00010\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}00100\\00010\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}00102\\00011\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}00102\\00011\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}00100\\00011\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}00100\\00011\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}00101\\00012\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}00101\\00012\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}00100\\00012\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}00100\\00012\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}00101\\00010\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}00101\\00010\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}00101\\00011\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}00101\\00011\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}00102\\00012\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}00102\\00012\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}00102\\00010\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}00102\\00010\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}00120\\00001\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}01000\\00001\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}01100\\00001\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}01010\\00001\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}01110\\00001\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}01000\\00100\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}01020\\00110\\\end{smallmatrix}\right)\), 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\(\left(\begin{smallmatrix}10211\\01110\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}10220\\01020\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}10212\\01122\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}10220\\01021\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}10212\\01120\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}10220\\01022\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}10212\\01121\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}10221\\01020\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}10210\\01122\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}10221\\01021\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}10210\\01120\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}10221\\01022\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}10210\\01121\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}10222\\01020\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}10211\\01122\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}10222\\01021\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}10211\\01120\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}10222\\01022\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}10211\\01121\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}10220\\01210\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}10220\\01211\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}10220\\01212\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}10221\\01210\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}10221\\01211\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}10221\\01212\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}10222\\01210\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}10222\\01211\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}10222\\01212\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}10220\\01221\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}10220\\01222\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}10220\\01220\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}10221\\01221\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}10221\\01222\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}10221\\01220\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}10222\\01221\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}10222\\01222\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}10222\\01220\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}10220\\01202\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}10220\\01200\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}10220\\01201\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}10221\\01202\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}10221\\01200\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}10221\\01201\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}10222\\01202\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}10222\\01200\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}10222\\01201\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}10201\\01210\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}10201\\01211\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}10201\\01212\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}10202\\01210\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}10202\\01211\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}10202\\01212\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}10200\\01210\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}10200\\01211\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}10200\\01212\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}10201\\01221\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}10201\\01222\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}10201\\01220\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}10202\\01221\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}10202\\01222\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}10202\\01220\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}10200\\01221\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}10200\\01222\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}10200\\01220\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}10201\\01202\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}10201\\01200\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}10201\\01201\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}10202\\01202\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}10202\\01200\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}10202\\01201\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}10200\\01202\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}10200\\01200\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}10200\\01201\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}10212\\01210\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}10212\\01211\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}10212\\01212\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}10210\\01210\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}10210\\01211\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}10210\\01212\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}10211\\01210\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}10211\\01211\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}10211\\01212\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}10212\\01221\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}10212\\01222\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}10212\\01220\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}10210\\01221\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}10210\\01222\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}10210\\01220\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}10211\\01221\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}10211\\01222\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}10211\\01220\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}10212\\01202\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}10212\\01202\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}10212\\01200\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}10212\\01200\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}10212\\01201\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}10212\\01201\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}10210\\01202\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}10210\\01202\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}10210\\01200\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}10210\\01200\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}10210\\01201\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}10210\\01201\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}10211\\01202\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}10211\\01202\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}10211\\01200\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}10211\\01200\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}10211\\01201\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}10211\\01201\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}11000\\00001\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}11100\\00001\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}11020\\00001\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}11120\\00001\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}11000\\00100\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}11020\\00110\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}11000\\00101\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}11022\\00111\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}11000\\00102\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}11021\\00112\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}11001\\00100\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}11021\\00110\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}11001\\00101\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}11020\\00111\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}11001\\00102\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}11022\\00112\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}11002\\00100\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}11022\\00110\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}11002\\00101\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}11021\\00111\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}11002\\00102\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}11020\\00112\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}11000\\00110\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}11012\\00121\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}11000\\00111\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}11011\\00122\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}11000\\00112\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}11010\\00120\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}11001\\00110\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}11010\\00121\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}11001\\00111\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}11012\\00122\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}11001\\00112\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}11011\\00120\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}11002\\00110\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}11011\\00121\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}11002\\00111\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}11010\\00122\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}11002\\00112\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}11012\\00120\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}11000\\00120\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}11000\\00121\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}11000\\00122\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}11001\\00120\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}11001\\00121\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}11001\\00122\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}11002\\00120\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}11002\\00121\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}11002\\00122\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}11010\\00100\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}11010\\00101\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}11010\\00102\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}11011\\00100\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}11011\\00101\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}11011\\00102\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}11012\\00100\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}11012\\00101\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}11012\\00102\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}11010\\00110\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}11020\\00121\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}11010\\00111\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}11022\\00122\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}11010\\00112\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}11021\\00120\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}11011\\00110\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}11021\\00121\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}11011\\00111\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}11020\\00122\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}11011\\00112\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}11022\\00120\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}11012\\00110\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}11022\\00121\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}11012\\00111\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}11021\\00122\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}11012\\00112\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}11020\\00120\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}11020\\00100\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}11020\\00101\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}11020\\00102\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}11021\\00100\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}11021\\00101\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}11021\\00102\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}11022\\00100\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}11022\\00101\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}11022\\00102\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}11210\\00001\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}11200\\00001\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}12000\\00001\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}12200\\00001\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}12020\\00001\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}12220\\00001\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}12000\\00100\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}12010\\00110\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}12000\\00101\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}12011\\00111\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}12000\\00102\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}12012\\00112\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}12001\\00100\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}12011\\00110\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}12001\\00101\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}12012\\00111\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}12001\\00102\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}12010\\00112\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}12002\\00100\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}12012\\00110\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}12002\\00101\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}12010\\00111\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}12002\\00102\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}12011\\00112\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}12000\\00110\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}12021\\00121\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}12000\\00111\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}12022\\00122\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}12000\\00112\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}12020\\00120\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}12001\\00110\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}12022\\00121\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}12001\\00111\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}12020\\00122\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}12001\\00112\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}12021\\00120\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}12002\\00110\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}12020\\00121\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}12002\\00111\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}12021\\00122\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}12002\\00112\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}12022\\00120\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}12000\\00120\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}12000\\00121\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}12000\\00122\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}12001\\00120\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}12001\\00121\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}12001\\00122\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}12002\\00120\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}12002\\00121\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}12002\\00122\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}12010\\00100\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}12021\\00110\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}12010\\00101\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}12022\\00111\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}12010\\00102\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}12020\\00112\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}12011\\00100\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}12022\\00110\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}12011\\00101\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}12020\\00111\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}12011\\00102\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}12021\\00112\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}12012\\00100\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}12020\\00110\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}12012\\00101\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}12021\\00111\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}12012\\00102\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}12022\\00112\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}12010\\00120\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}12010\\00121\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}12010\\00122\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}12011\\00120\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}12011\\00121\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}12011\\00122\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}12012\\00120\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}12012\\00121\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}12012\\00122\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}12020\\00100\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}12020\\00101\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}12020\\00102\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}12021\\00100\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}12021\\00101\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}12021\\00102\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}12022\\00100\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}12022\\00101\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}12022\\00102\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}12110\\00001\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}12120\\00001\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}00010\\00001\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}00010\\00001\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}00010\\00001\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}00010\\00001\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}00010\\00001\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}00010\\00001\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}00010\\00001\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}00010\\00001\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}00010\\00001\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}10000\\00001\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}10010\\00001\\\end{smallmatrix}\right)\), \(\left(\begin{smallmatrix}10020\\00001\\\end{smallmatrix}\right)\).

References↩︎

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1. Department of Mathematics: Analysis, Logic and Discrete Mathematics, Ghent University, 9000 Ghent, Belgium.  E-mail: jozefien.dhaeseleer@ugent.be↩︎

2. Department of Mathematics, University of Bayreuth, 95440 Bayreuth, Germany.↩︎

3. Given a linear \([n,k]_q\) code \(C\) with generator matrix \(G\), we can interpret its columns as \(1\)-dimensional vector spaces of \(\mathbb{F}_q^k\) or points in \(\mathrm{PG}(k-1,q)\).↩︎

4. While the geometric equivalent of linear or additive codes is very handy for many situations, here the coding theory version looks more nicely. In particular, denoting the minimum length \(n\) of an \([n,k,d]_q\) code by \(\tilde{n}_q(k,d)\), we have \(\lim_{d\to\infty} \tilde{n}_q(k,d)-g_q(k,d)=0\). There is a similar formulation for additive codes, see [9].↩︎