Cyclic large sets of Steiner triple systems of order 15

Phelps, Kevin T.

doi:10.1090/S0025-5718-1990-1035942-1

Cyclic large sets of Steiner triple systems of order $15$
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Math. Comp. 55 (1990), 821-824 Request permission

Abstract:

We examine a class of large sets of Steiner triple systems of order 15 having an automorphism consisting of two fixed points and a 13-cycle. We exhibit all members of this class: there are 256 nonisomorphic systems. We examined these members for initial configurations which could lead to a large set of Steiner quadruple systems of order 16 and established that no large set exists having three fixed points and a 13-cycle.

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