New Upper Bounds on Sizes of Permutation Arrays

A permutation array(or code) of length n and distance d, denoted by (n, d) PA, is a set of permutations C from some fixed set of n elements such that the Hamming distance between distinct members x,y ∈ C is at least d. Let P (n, d) denote the maximum size of an (n, d) PA. New upper bounds on P (n, d) are given. For constant α, β satisfying certain conditions, whenever d = βn, the new upper bounds are asymptotically better than the previous ones.