t-designs

This page contains a collection of t-designs, with an emphasis on balanced incomplete-block designs (equivalently 2-(v,k,lambda) designs with k<v). The files downloadable from this page contain lists of pairwise non-isomorphic t-designs for the given parameters t,v,b,r,k,L(=lambda). They are in DTRS external representation protocol version 2.0 format, compressed by bzip2. Each file has content types i, c, g and s, which mean that each design in that file has, respectively, <indicators>, <combinatorial_properties>, <automorphism_group> and <statistical_properties> subtrees. Certain files also have content type a, which means that all t-designs (up to isomorphism) with the given parameters are in that file. For each resolvable t-design in the files on this page, at least one resolution is given.

For 6<=v<=20, r<=20 and 3<=k<=v/2, we give at least one design for each parameter list (2,v,b,r,k,L) for which a 2-design exists. Moreover, for these parameters, we include, up to isomorphism, at least all cyclic and all 1-rotational 2-designs.

In addition, we give the projective planes PG(2,q) for q=4,5,7,8, the affine planes AG(2,q) for q=5,7,8, the cyclic and the 1-rotational 2-(v,3,1) designs for 21<=v<=31, the cyclic and the 1-rotational 2-(21,4,3) designs, the cyclic and the 1-rotational 2-(22,4,2) designs, the 2-(31,4,2) designs invariant under a group of order 93, the 5-(12,6,1), 4-(11,5,1) and 3-(10,4,1) designs associated with the small Mathieu group M12, and the 5-(24,8,1), 4-(23,7,1) and 3-(22,6,1) designs associated with the large Mathieu group M24.

No particular ordering of designs within a file should be assumed.

Note: The naming and ordering of designs and some isomorphism class representatives changed when this page was overhauled on 25 November 2004.

Number of files = 99

t v b r k L content type # designs
2 6 10 5 3 2 i c g s a 1 download
2 6 20 10 3 4 i c g s a 4 download
2 6 30 15 3 6 i c g s a 6 download
2 6 40 20 3 8 i c g s a 13 download
2 7 7 3 3 1 i c g s a 1 download
2 7 14 6 3 2 i c g s a 4 download
2 7 21 9 3 3 i c g s a 10 download
2 7 28 12 3 4 i c g s a 35 download
2 7 35 15 3 5 i c g s a 109 download
2 7 42 18 3 6 i c g s a 418 download
2 8 14 7 4 3 i c g s a 4 download
2 8 28 14 4 6 i c g s a 2310 download
2 9 12 4 3 1 i c g s a 1 download
t v b r k L content type # designs
2 9 18 8 4 3 i c g s a 11 download
2 9 24 8 3 2 i c g s a 36 download
2 9 36 12 3 3 i c g s 9 download
2 9 36 16 4 6 i c g s 31 download
2 9 48 16 3 4 i c g s 19 download
2 9 60 20 3 5 i c g s 28 download
2 10 15 6 4 2 i c g s a 3 download
2 10 18 9 5 4 i c g s 2 download
2 10 30 9 3 2 i c g s a 960 download
2 10 30 12 4 4 i c g s 13 download
2 10 36 18 5 8 i c g s 40 download
2 10 45 18 4 6 i c g s 105 download
2 10 60 18 3 4 i c g s 30 download
t v b r k L content type # designs
2 11 11 5 5 2 i c g s a 1 download
2 11 22 10 5 4 i c g s 7 download
2 11 33 15 5 6 i c g s 11 download
2 11 44 20 5 8 i c g s 151 download
2 11 55 15 3 3 i c g s 21 download
2 11 55 20 4 6 i c g s 348 download
2 12 22 11 6 5 i c g s 5 download
2 12 33 11 4 3 i c g s 10 download
2 12 44 11 3 2 i c g s 9 download
2 13 13 4 4 1 i c g s a 1 download
2 13 26 6 3 1 i c g s a 2 download
2 13 26 8 4 2 i c g s 4 download
2 13 26 12 6 5 i c g s 7 download
t v b r k L content type # designs
2 13 39 12 4 3 i c g s 26 download
2 13 39 15 5 5 i c g s 76 download
2 13 52 12 3 2 i c g s 21 download
2 13 52 16 4 4 i c g s 294 download
2 13 65 20 4 5 i c g s 571 download
2 13 78 18 3 3 i c g s 152 download
2 14 26 13 7 6 i c g s 7 download
2 15 15 7 7 3 i c g s a 5 download
2 15 30 14 7 6 i c g s 31 download
2 15 35 7 3 1 i c g s a 80 download
2 15 35 14 6 5 i c g s 8 download
2 15 42 14 5 4 i c g s 85 download
2 15 70 14 3 2 i c g s 62 download
t v b r k L content type # designs
2 16 16 6 6 2 i c g s a 3 download
2 16 20 5 4 1 i c g s a 1 download
2 16 24 9 6 3 i c g s 1 download
2 16 30 15 8 7 i c g s 24 download
2 16 32 12 6 4 i c g s 16 download
2 16 40 10 4 2 i c g s 6 download
2 16 40 15 6 5 i c g s 25 download
2 16 48 15 5 4 i c g s 294 download
2 16 48 18 6 6 i c g s 776 download
2 16 60 15 4 3 i c g s 450 download
2 16 80 15 3 2 i c g s 122 download
2 16 80 20 4 4 i c g s 5872 download
2 17 34 16 8 7 i c g s 28 download
t v b r k L content type # designs
2 17 68 16 4 3 i c g s 542 download
2 17 68 20 5 5 i c g s 7260 download
2 18 34 17 9 8 i c g s 21 download
2 18 51 17 6 5 i c g s 582 download
2 18 102 17 3 2 i c g s 186 download
2 19 19 9 9 4 i c g s a 6 download
2 19 38 18 9 8 i c g s 108 download
2 19 57 9 3 1 i c g s 4 download
2 19 57 12 4 2 i c g s 22 download
2 19 57 18 6 5 i c g s 1535 download
2 19 114 18 3 2 i c g s 665 download
2 20 38 19 10 9 i c g s 32 download
2 20 76 19 5 4 i c g s 10067 download
t v b r k L content type # designs
2 20 95 19 4 3 i c g s 10040 download
2 21 21 5 5 1 i c g s a 1 download
2 21 70 10 3 1 i c g s 7 download
2 21 105 20 4 3 i c g s 26320 download
2 22 77 14 4 2 i c g s 43 download
2 25 30 6 5 1 i c g s a 1 download
2 25 100 12 3 1 i c g s 12 download
2 27 117 13 3 1 i c g s 44 download
2 31 31 6 6 1 i c g s a 1 download
2 31 155 15 3 1 i c g s 80 download
2 31 155 20 4 2 i c g s 43 download
2 49 56 8 7 1 i c g s a 1 download
2 57 57 8 8 1 i c g s a 1 download
t v b r k L content type # designs
2 64 72 9 8 1 i c g s a 1 download
2 73 73 9 9 1 i c g s a 1 download
3 10 30 12 4 1 i c g s a 1 download
3 22 77 21 6 1 i c g s a 1 download
4 11 66 30 5 1 i c g s a 1 download
4 23 253 77 7 1 i c g s a 1 download
5 12 132 66 6 1 i c g s a 1 download
5 24 759 253 8 1 i c g s a 1 download


Last updated: 2005-07-22 07:49:36.406216