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Designs from projective planes and PBD bases
Author(s) -
Greig Malcolm
Publication year - 1999
Publication title -
journal of combinatorial designs
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.618
H-Index - 34
eISSN - 1520-6610
pISSN - 1063-8539
DOI - 10.1002/(sici)1520-6610(1999)7:5<341::aid-jcd5>3.0.co;2-1
Subject(s) - mathematics , prime (order theory) , combinatorics , projective test , order (exchange) , block (permutation group theory) , prime power , spectrum (functional analysis) , resolution (logic) , discrete mathematics , pure mathematics , computer science , physics , finance , quantum mechanics , artificial intelligence , economics
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 ( q 2 + 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 ( P 7 , 1), where P 7 is odd prime powers ≥ 7; some constructions showing the inessential nature of values in E a + , where E a +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