The Asymptotic Behaviour of Equidistant Permutation Arrays
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An equidistant permutation array (EPA) A(r λ v) is a v × r array defined on a set V of r symbols such that every row is a permutation of V and any two distinct rows have precisely λ common column entries. Define R(r, λ) to be the largest value of v for which there exists an A (r, λ; v). Deza [2] has shown that where n = r – λ. Bolton [1] has shown that (*) In this paper, we show that equality holds in (*) for λ > ┌n/3┐(n 2 + n). In order to do this we require several more definitions.
[1] Scott A. Vanstone,et al. Pairwise "Orthogonal Generalized Room Squares" and Equidistant Permutation Arrays , 1978, J. Comb. Theory, Ser. A.
[2] Michel Deza. Matrices Dont Deux Lignes Quelconque Coïncident dans un Nombre Donne de Positions Communes , 1976, J. Comb. Theory, Ser. A.