Two new infinite families of extremal class-uniformly resolvable designs

• Published in: Journal of combinatorial designs Vol. 16; no. 3; pp. 213 - 220
• Main Authors: Dinitz, J.H., Ling, Alan C.H.
• Format: Journal Article
• Language: English
• Published: Hoboken Wiley Subscription Services, Inc., A Wiley Company 01-05-2008
• Subjects: CURD; PBD; uniformly resolvable designs
• ISSN: 1063-8539; 1520-6610
• DOI: 10.1002/jcd.20165

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 ≤ (3p3)2 and v ≤  (p2)2 where pi denotes the number of blocks of size i for i = 2, 3. They then constructed an infinite class of extremal CURDs with v = (3p3)2 when p3 is odd and an infinite class with v = (p2)2 when p2 ≡ 2 (mod 6). In this note, we construct two new infinite families of extremal CURDs, when v = (3p3)2 for all p3 ≥ 1 and when v = (p2)2 with p2 ≡ 0 (mod 3) except possibly when p2 = 12. © 2007 Wiley Periodicals, Inc. J Combin Designs 16: 213–220, 2008