  We report here on the results of numerical searches for PPT states with
specified ranks for density matrices and their partial transpose. The study
includes several bipartite quantum systems of low dimensions. For a series of
ranks extremal PPT states are found. The results are listed in tables and
charted in diagrams. Comparison of the results for systems of different
dimensions reveal several regularities. We discuss lower and upper bounds on
the ranks of extremal PPT states.
