Steiner Systems S(2,4,25)
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).
The paper in which these results were announced is The Complete
Classification of Steiner Systems S(2,4,25)
Journ. Comb. Designs 4 (1996), no. 4, 295-300.