Group Divisible Designs with Block Size Five from Clatworthy's Table

Abstract

Clatworthy’s table [2] lists thirty seven designs with block size 5 where the number of groups is at the most equal to block size. Mwesigwa, Sarvate and Zhang have generalized one of these designs in a recent paper [16]. In this note we generalize all but one such designs listed in the table. As an aside, we prove that GDD (n, 4, 5; 9n n−1 , 2) with intersection pattern (1, 4) does not exist for any n except for n = 4.1991