An infinite class of fibres in CURDs with block sizes two and three

✍ Scribed by Melissa S. Keranen; Rolf S. Rees; Alan C.H. Ling

• Publisher: John Wiley and Sons
• Year: 2003
• Tongue: English
• Weight: 207 KB
• Volume: 12
• Category: Article
• ISSN: 1063-8539
• DOI: 10.1002/jcd.10053

✦ Synopsis

Abstract

Class‐uniformly resolvable designs (CURDs) are introduced by Lamken et al. Discrete Math 92 (1991) 197–209. In Wevrick and Vanstone, J Combin Designs 4 (1996) 177–202, a classification scheme is developed based on the ratio a:b of pairs to triples. Asymptotic existence results are obtained when (a,b) = (1,2__n__), n ≥ 1 and when (a,b) = (9,2). The authors also obtain partial results on the existence of CURDs when (a,b) = (1,2__n__), 1 ≤ n ≤ 5, (a,b) = (3, 6__u__ − 2), u ≥ 1 and when (a,b) ∈ {(1,1), (3,1), (7,2), (3,4), (9,2)}. In Danziger and Stevens, J Combin Designs 9 (2001), 79–99, the necessary and sufficient conditions for CURDs when (a,b) = (3,1) are completely settled. In this article, we obtain a necessary and sufficient condition when (a,b) = (3__m__, 1) for all m > 1. © 2003 Wiley Periodicals, Inc.