An upper bound on the number of Steiner triple systems

Richard Wilson conjectured in 1974 the following asymptotic formula for the number of n -vertex Steiner triple systems: Our main result is that The proof is based on the entropy method. As a prelude to this proof we consider the number F(n) of 1 -factorizations of the complete graph on n vertices. Using the Kahn-Lovász theorem it can be shown that We show how to derive this bound using the entropy method. Both bounds are conjectured to be sharp.