Shrikhande  and Roy  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  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.
"The Dual of a Balanced Incomplete Block Design." Ann. Math. Statist. 31 (3) 779 - 785, September, 1960. https://doi.org/10.1214/aoms/1177705804