Wilson's joint asymptotic enumeration conjecture for Steiner triple systems and 1-factorizations

Let $STS(n)$ be the number of Steiner triple systems on $n$ points and let $F(n)$ be the number of 1-factorizations of the complete graph $K_n$. Wilson's joint asymptotic conjecture.

$$STS(n)=\left(\left(1+o(1)\right)\frac{n}{e^2}\right)^{\frac{n^2}{6}},$$ $$F(n)=\left(\left(1+o(1)\right)\frac{n}{e^2}\right)^{\frac{n^2}{2}}.$$

The first estimate is Wilson's conjecture for Steiner triple systems, and the paper proves the corresponding asymptotic upper bounds for both quantities. Matching lower bounds, and hence the displayed asymptotics as equalities, are the unresolved aspect in the source.