Class-uniformly resolvable group divisible structures. I: Resolvable group divisible designs (Q1883633)

Summary: We consider class-uniformly resolvable group divisible designs, which are resolvable group divisible designs in which each of the resolution classes has the same number of blocks of each size. We derive the fully general necessary conditions including a number of extremal bounds. We present some general constructions including a novel construction for shrinking the index of a master design. We construct a number of infinite families, primarily with block sizes \(2\) and \(k\), including some extremal cases.