Perpendicular Arrays are ordered combinatorial structures, which recently have found applications in cryptography. A fundamental construction uses as ingredients combinatorial designs and uniformly t-homogeneous sets of permutations. We study the latter type of objects. These may also be viewed as generalizations of t-homogeneous groups of permutations. Several construction techniques are given. Here we concentrate on the optimal case, where the number of permutations attains the lower bound. We obtain several new optimal such sets of permutations. Each example allows the construction of infinite families of perpendicular arrays.
['Jürgen Bierbrauer', 'Stephen Black', 'Yves Edel']
Some t -Homogeneous Sets of Permutations