Class-uniformly resolvable group divisible structures. II: Frames (Q1883634)

Summary: We consider class-uniformly resolvable frames (CURFs), which are group divisible designs with partial resolution classes subject to the class-uniform condition. We derive the necessary conditions, including extremal bounds, build the foundation for general CURF constructions, including a frame variant of the \(\lambda\) blow-up construction from Part I [Electron. J. Comb. 11, No. 1, Research paper R23, 13p. (2004)]. We also establish a PBD-closure result. For CURFs with blocks of size two and three we determine the existence of CURFs of type \(g^u\), completely for \(g=3\), with a small list of exceptions for \(g=6\), asymptotically for \(g=4,5\) and give some other infinite families.