Publications 2-designs Two Graphs Hadamard
Matrices Regular graphs
eigenvalues Steiner S(2,4,25) Strongly Regular
graphs on at
most 64 vertices Symmetric
After a lengthy computer investigation into Steiner systems
S(2,4,25) (the same thing as a 2-(25,4,1) design), I can now announce
that they have been completely classified. The result is that there are
exactly 18 such Steiner systems, 16 of which have a non-trivial
automorphism group and were already known . The new part of my
investigation was the complete determination of those with a
trivial automorphism group. If you would like a copy of these
18 designs you can get them from S(2,4,25)
(in zero-one form).
These results were announced in .
 E S Kramer, S S Maglivers and R Mathon, The Steiner Systems S(2,4,25) with Nontrivial Automorphism Group, J. Discr. Math. 77 (1989), pp 137-157.
 E Spence, The Complete Classification of Steiner Systems S(2,4,25) Journ. Comb. Designs 4 (1996), no. 4, 295-300.