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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 3.0 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.