Designs and perfect codes

A Steiner triple system of order n (briefly STS(n)) is a family of 3-element blocks (subsets or triples) of the set N = {1, 2,..., n} such that each not ordered pair of elements of N appears in exactly one block. Two STS-s of order n are called isomorphic if there exists a permutation on the set N which transforms them into one another. It is well known that STS(n) exists if and only if n equivalent to 1 or 3 (mod 6). The number N(n) of nonisomorphic Steiner triple systems STS-s of order n satisfies to the following bounds (e(-5)n)(n2/6) <= N(n) <= (e(-1/2)n)(n2)/(6). The lower bound was proved by Egorychev in 1980 using the result on permanents of double stochastic matrices, see [1,2], the upper bound is straightforward. It is well known that for n = 15 there are 80 nonisomorphic Steiner triple systems of order 15.