Construction of three-associate class PBIB designs by generating a set of square matrices

Abstract

The present paper deals with the construction of three-associate class PBIB designs. For this, we have first discussed a procedure to generate a set of square matrices. The construction of this set of matrices has been completely generalized. Then using this set of matrices, we have proposed a new three-associate class association scheme based on which we have constructed some series of PBIB designs. The complementary designs of the proposed PBIB designs have also been discussed. At the end of the paper, a table has been given which enlists some of the PBIB designs constructed in this paper.