Posets on up to 16 Points

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