Abstract
Abstract In this paper, we determine some results regarding the parameter D i (n, k), i=1, 2, 3, 4 where D1(n, k) is the maximum number of latin squares such that any two of them intersect in k entries, which occurring in each of the latin squares, and D 2(n, k), D 3(n, k), D 4(n, k) are similar results for idempotent latin squares, idem-potent commutative latin squares, and latin cubes respectively. Moreover, we apply some of the above results to obtain some similar results in Steiner triple systems and Steiner quadruple systems [7, 12].
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