Shah  obtained an upper bound for the number of disjoint blocks in certain PBIB designs. The results obtained there  were based on theorems given in References , , and . It should be pointed out here that theorems on Semi-Regular Group Divisible designs  are also implicitly given by Saraf . 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.
"On the Block Structure of Singular Group Divisible Designs." Ann. Math. Statist. 37 (5) 1398 - 1400, October, 1966. https://doi.org/10.1214/aoms/1177699284