Bounds for permutation arrays under Kendall Tau metric

Permutation arrays under the Kendall-[Formula: see text] metric have been considered for error-correcting codes. Given [Formula: see text] and [Formula: see text], the task is to find a large permutation array of permutations on [Formula: see text] symbols with pairwise Kendall-[Formula: see text] distance at least [Formula: see text]. Let [Formula: see text] denote the maximum size of any permutation array of permutations on [Formula: see text] symbols with pairwise Kendall-[Formula: see text] distance [Formula: see text]. New algorithms and several theorems are presented, giving improved lower bounds for [Formula: see text]. Also, [Formula: see text]-arrays are defined, which are permutation arrays on [Formula: see text] symbols with Kendall-[Formula: see text] distance [Formula: see text], with the restriction that symbols [Formula: see text] appear in increasing order. Let [Formula: see text] denote the maximum size of any [Formula: see text]-array. For example, [Formula: see text]-arrays are useful for recursively computing lower bounds for [Formula: see text]. Lower and upper bounds are given for [Formula: see text].