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 withλ2=λ1+1, a group divisible design with group size two andλ2=λ1+1>1, a design based on a triangular scheme andv=10 andλ1=λ2+1, a design with anL2 scheme andλ2=λ1+1, a design with anLs scheme,v=(s+1)2, andλ2=λ1+1, wheres is a positive integer, or a design with a cyclic schemev=5, andλ1=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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