Uniformly resolvable pairwise balanced designs with blocksizes two and three
Journal of Combinatorial Theory Series A
Resolvable group divisible designs with block size four
Discrete Mathematics
On Group-Divisible Designs with Block Size Four and Group-Type gum1
Designs, Codes and Cryptography
Resolvable group divisible designs with block size four and group size six
Discrete Mathematics
Resolvable maximum packings with quadruples
Designs, Codes and Cryptography
Handbook of Combinatorial Designs, Second Edition (Discrete Mathematics and Its Applications)
Handbook of Combinatorial Designs, Second Edition (Discrete Mathematics and Its Applications)
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A Uniformly Resolvable Design (URD) is a resolvable design in which each parallel class contains blocks of only one block size k, such a class is denoted k -pc and for a given k the number of k -pcs is denoted r k . In this paper we consider the case of block sizes 3 and 4. The cases r 3 = 1 and r 4 = 1 correspond to Resolvable Group Divisible Designs (RGDD). We prove that if a 4-RGDD of type h u exists then all admissible {3, 4}-URDs with 12hu points exist. In particular, this gives existence for URD with v 驴 0 (mod 48) points. We also investigate the case of URDs with a fixed number of k -pc. In particular, we show that URDs with r 3 = 4 exist, and that those with r 3 = 7, 10 exist, with 11 and 12 possible exceptions respectively, this covers all cases with 1 r 3 驴 10. Furthermore, we prove that URDs with r 4 = 7 exist and that those with r 4 = 9 exist, except when v = 12, 24 and possibly when v = 276. In addition, we prove that there exist 4-RGDDs of types 2 142, 2 346 and 6 54. Finally, we provide four {3,5}-URDs with 105 points.