Permutation codes invariant under isometries

The symmetric group Sn on n letters is a metric space with respect to the Hamming distance. The corresponding isometry group is well known to be isomorphic to the wreath product Sn oS2. A subset of Sn is called a permutation code or a permutation array, and the largest possible size of a permutation code with minimum Hamming distance d is denoted by M(n, d). Using exhaustive search by computer on sets of orbits of isometry subgroups U we are able to determine serveral new lower bounds for M(n, d) for n ≤ 22. The codes are given by the group U and representatives of the U -orbits. ∗Supported in part by the Academy of Finland under Grant No. 132122.