The complete classification of Steiner systems S(2, 4, 25)

We describe an algorithm that was used to classify completely all Steiner systems S(2, 4, 25). The result is that in addition to the 16 nonisomorphic designs with nontrivial automorphism group already known, there are precisely two such nonisomorphic designs with a trivial automorphism group. © 1996 John Wiley & Sons, Inc.