The Asymptotic Behaviour of Equidistant Permutation Arrays

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.