Designs from projective planes and PBD bases

Abstract

The essential theme of this article is the exploitation of known configurations in projective planes in order to construct pairwise balanced designs. Among the results shown are (q2 + 1)/2 ∈ B((q + 1)/2, 2) for all odd prime powers q; the resolution of 31 of the Mullin and Stinson's open cases in the spectrum of B(P7, 1), where P7 is odd prime powers ≥ 7; some constructions showing the inessential nature of values in E, where E are PBD generating sets containing values equal to 1 mod(a) for 5 ≤ a ≤ 7; some constructions with block sizes being prime powers ≥ 8, yielding 7 MOLS of order 158 and 9 MOLS of order 254; and some designs on 28, 38, 42, 56, 63, 68, 72, and 156 points with interesting block sizes. © 1999 John Wiley & Sons, Inc. J Combin Designs 7: 341–374, 1999