On the comparison of PBIB designs with two associate classes

A method to compare two-associate-class PBIB designs is discussed. As an application, it is shown that ifd ^* is a group-divisible design withλ ₂=λ₁+1, a group divisible design with group size two andλ ₂=λ₁+1>1, a design based on a triangular scheme andv=10 andλ ₁=λ₂+1, a design with anL ₂ scheme andλ ₂=λ₁+1, a design with anL _s scheme,v=(s+1) ², andλ ₂=λ₁+1, wheres is a positive integer, or a design with a cyclic schemev=5, andλ ₁=λ₂±1, thend ^* is optimum with respect to a very general class of criteria over all the two-associate-class PBIB designs with the same values ofv, b andk asd ^*. The best two-associate-class PBIB design, however, is not necessarily optimal over all designs. This paper was prepared with the support of Office of Naval Research Contract No. N00014-75-C-0444/NR 042-036 and National Science Foundation Grant No. MCS-79-09502.