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The spectrum of additive BIB designs

✍ Scribed by M. Sawa; K. Matsubara; D. Matsumoto; H. Kiyama; S. Kageyama

Publisher: John Wiley and Sons
Year: 2007
Tongue: English
Weight: 201 KB
Volume: 15
Category: Article
ISSN: 1063-8539
DOI: 10.1002/jcd.20147

No coin nor oath required. For personal study only.

✦ Synopsis

Abstract

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

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