Two new infinite families of extremal class-uniformly resolvable designs

✍ Scribed by J.H. Dinitz; Alan C.H. Ling

• Publisher: John Wiley and Sons
• Year: 2008
• Tongue: English
• Weight: 114 KB
• Volume: 16
• Category: Article
• ISSN: 1063-8539
• DOI: 10.1002/jcd.20165

✦ Synopsis

Abstract

In 1991, Lamken et al. [7] introduced the notion of class‐uniformly resolvable designs, CURDs. These are resolvable pairwise balanced designs PBD(v, K, λ) in which given any two resolution classes C and C', for each k ∈ K the number of blocks of size k in C is equal to the number of blocks of size k in C'. Danzinger and Stevens showed that if a CURD has v points, then v ≤ (3__p__~3~)^2^ and v ≤  (p~2~)^2^ where p~i~ denotes the number of blocks of size i for i = 2, 3. They then constructed an infinite class of extremal CURDs with v = (3__p__~3~)^2^ when p~3~ is odd and an infinite class with v = (p~2~)^2^ when p~2~ ≡ 2 (mod 6). In this note, we construct two new infinite families of extremal CURDs, when v = (3__p__~3~)^2^ for all p~3~ ≥ 1 and when v = (p~2~)^2^ with p~2~ ≡ 0 (mod 3) except possibly when p~2~ = 12. © 2007 Wiley Periodicals, Inc. J Combin Designs 16: 213–220, 2008