Two New Infinite Families of Extremal Class-Uniformly Resolvable Designs J. H. Dinitz, 1 Alan C. H. Ling 2 1 Department of Mathematics and Statistics, University of Vermont, Burlington, Vermont, E-mail: jeff.dinitz@uvm.edu 2 Department of Computer Science University of Vermont Burlington, Vermont, E-mail: aling@cems.uvm.edu Received October 6, 2006; revised April 19, 2007 Published online 18 June 2007 in Wiley InterScience (www.interscience.wiley.com). DOI 10.1002/jcd.20165 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 ≤ (3p 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 = (3p 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 = (3p 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 Keywords: PBD; CURD; uniformly resolvable designs 1. INTRODUCTION Let K be a set of positive integers. A pairwise balanced design PBD(v, K, 1) is a pair (V, B) where |V |= v, and B is a collection of subsets of V called blocks. Each subset has size k ∈ K and each pair of points of V occurs exactly one time in the blocks. A group divisible design (or GDD) is a triple (X, G, B) which satisfies the following properties: 1. G is a partition of a set X (of points) into subsets called groups, 2. B is a set of subsets of X (called blocks) such that a group and a block contain at most one common point, 3. every pair of points from distinct groups occurs in a unique block. © 2007 Wiley Periodicals, Inc. 213