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Four different views of Glasgow University Tower

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 [1]. 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 [2].

[1] 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.

[2] E Spence, The Complete Classification of Steiner Systems S(2,4,25) Journ. Comb. Designs 4 (1996), no. 4, 295-300.