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Let STS(n) denote the number of Steiner triple systems on n vertices, and letF(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.

An Upper bound on the number of Steiner triple systems