On the Block Structure of Singular Group Divisible Designs

Abstract

Shah [5] obtained an upper bound for the number of disjoint blocks in certain PBIB designs. The results obtained there [5] were based on theorems given in References [1], [3], and [6]. It should be pointed out here that theorems on Semi-Regular Group Divisible designs [5] are also implicitly given by Saraf [4]. In this note, the similar results are given for Singular Group Divisible (SGD) designs and the main tool used to establish them is Theorem 3.1 given below.