Uniformly resolvable pairwise balanced designs with blocksizes two and three

A uniformly resolvable pairwise balanced design is a pairwise balanced design whose blocks can be resolved into parallel classes in such a way that all blocks in a given parallel class have the same size. We are concerned here with designs in which each block has size two or three, and we prove that the obvious necessary conditions on the existence of such designs are also sufficient, with two exceptions, corresponding to the non-existence of Nearly Kirkman Triple Systems of orders 6 and 12. 6 1987 Academic Press, Inc.