In this article we describe a very efficient method to construct pairwise nonisomorphic posets (equivalently, T0 topologies). We also give the results obtained by a computer program based on this algorithm, in particular the numbers of nonisomorphic posets on 15 and 16 points and the numbers of labelled posets and topologies on 17 and 18 points.
Gunnar Brinkmann, Brendan D. McKay