An Upper bound on the number of Steiner triple systems
  Let STS(n) denote the number of Steiner triple systems on n vertices, and let F(n) denote the number of 1-factorizations of the complete graph on n vertices. We prove the following upper bound.   STS(n) <= ((1 + o(1)) (n/e^2))^(n^2/6)   F(n) <= ((1 + o(1)) (n/e^2))^(n^2/2)   We conjecture that the bound is sharp. Our main tool is the entropy method. 
Nathan Linial and Zur Luria
math.CO