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2. Definitions. A partially balanced incomplete block design with two associate classes having the parameters v, b, r, k, Xi, ni, Pk (i, j, k = 1, 2) is an arrangement of v varieties into b blocks, together with a relationship called association defined for every pair of varieties satisfying the following conditions: (i) Each of the v varieties occurs in r blocks. Each block contains k varieties and no variety appears more than once in a block. (ii) Every pair of varieties are either first or second associates. Each variety has ni first associates and n2 second associates. (iii) Any pair of varieties which are ith associates occur together in exactly Xi blocks (i= 1, 2). (iv) For every pair of varieties which are ith associates, the number of varieties common to the jth associates of the first and the kth associates of the second in pjk (i, j, k = 1, 2). It has been shown by Bose and Nair [2] that the parameters Plh, nz (i =1, 2) determine the matrices Pi (i = 1, 2) uniquely. The following relations are proved:

A three parameter family of partially balanced incomplete block designs with two associate classes