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

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.