Bounds for the Number of Common Treatments Between Any Two Blocks of Certain PBIB Designs

Abstract

In an earlier paper [4], the author has given upper bounds for the number of disjoint blocks in (i) Semi-regular GD designs, (ii) certain PBIB designs with two associate classes having triangular association scheme, (iii) certain PBIB designs with two associate classes having $L_2$ association scheme and (iv) certain PBIB designs with three associate classes having rectangular association scheme. In this paper, we give bounds for the number of common treatments between any two blocks of the above-mentioned PBIB designs. The main tools used to establish the results of this paper are the theorems proved by (i) Bose and Connor [1], (ii) Raghavarao [3], and (iii) Vartak [6].