In this paper we construct pairwise balanced designs (PBDs) having block sizes which are prime powers congruent to 1 modulo 6. Such a PBD containsn = 6r + 1 points, for some positive integerr. We show that this condition is sufficient forn ? 1927, with at most 31 possible exceptions below this value. As an immediate corollary, we prove that there exists a pair of orthogonal Steiner triple systems of ordern, for the same values ofn.
['Ronald C. Mullin', 'Douglas R. Stinson']
Pairwise balanced designs with block sizes 6t + 1