Abstract
In a balanced incomplete block (BIB) design with parameters v, b, r, k and 1, if the blocks can be separated into r sets of n blocks each (b = nr) such that each set of n blocks forms a complete replication, the design is called resolvable. Moreover, if two blocks belonging to different sets have the same number of treatments in common, the design is called affine resolvable. Bose [2] proved that if a resolvable BIB design with parameters v, b, r, k and 2 exists, then b ? v + r1 and that if for a resolvable BIB design the condition b = v+r-1 holds, then the design is affine resolvable and further, the number of treatments common to any two blocks of different sets is k2/v, so that k2 must be divisible by v. That is to say, necessary conditions for the existence of a resolvable BIB design are that
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