Abstract
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.
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Mullin, R.C., Stinson, D.R. Pairwise balanced designs with block sizes 6t + 1. Graphs and Combinatorics 3, 365–377 (1987). https://doi.org/10.1007/BF01788559
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DOI: https://doi.org/10.1007/BF01788559