Two new infinite families of extremal class‐uniformly resolvable designs

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