On the comparison of PBIB designs with two associate classes
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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.
KeywordsGeneralize Type Adjacency Matrix Small Eigenvalue Association Scheme Balance Incomplete Block Design
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