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The spectrum of additive BIB designs
Author(s) -
Sawa M.,
Matsubara K.,
Matsumoto D.,
Kiyama H.,
Kageyama S.
Publication year - 2007
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/jcd.20147
Subject(s) - mathematics , combinatorics , prime (order theory) , integer (computer science) , combinatorial design , prime power , discrete mathematics , computer science , programming language
In this article, the existence of additive BIB designs is discussed with direct and recursive constructions, together with investigation of a property of resolvability. Such designs can be used to construct infinite families of BIB designs. In particular, we obtain a series of B( s n , ts m , λ t ( ts m − 1) ( s n‐m − 1)/[2( s m − 1)]) for any positive integer λ, such that s n ( s n − 1) λ ≡ 0 (mod s m ( s m − 1) and for any positive integer t with 2 ≤ t ≤ s n‐m , where s is an odd prime power. Connections between additive BIB designs and other combinatorial objects such as multiply nested designs and perpendicular arrays are discussed. A construction of resolvable BIB designs with v = 4 k is also proposed. © 2007 Wiley Periodicals, Inc. J Combin Designs 15: 235–254, 2007