The Dual of a Balanced Incomplete Block Design

Abstract

Shrikhande [9] and Roy [7] have shown that certain Balanced Incomplete Block Designs (BIBDs) can be dualised to give Partially Balanced Incomplete Block Designs (PBIBDs) with exactly two associate classes. Roy and Laha [8] have obtained a necessary and sufficient condition for the dual of a BIBD to be a PBIBD with two associate classes. In this paper, a general result regarding the dual of a BIBD is established and the results of Shrikhande and Roy are obtained as particular cases. An illustration to show the use of the result when the dual is not a 2-associate PBIBD is also given.