On the number of steiner triple systems

We obtain a new lower estimate for the number $N(n)$ of nonisomorphic Steiner triple systems of order $n$:
$$ N(n)\ge n^{\frac{n^2}{12}-O\bigl(\frac{n^2}{\log n}\bigr)}. $$
This makes it possible to show that $\log N(n)$ is of order $n^2\log n$.