Bounds for permutation arrays

A permutation array (P.A.) defined on an r-set of symbols V is a v×r array of rows each of which is a permutation of the symbols of V and such that any two distinct rows have at most (at least) λ common column entries. We list all known bounds for such arrays and make improvements in certain cases. We consider, at length, the case when every pair of distinct rows of the P.A. have precisely λ common column entries.