A Recursive Construction of t-Wise Uniform Permutations

We present a recursive construction of a (2t + 1)-wise uniform set of permutations on 2n objects using a (2t+1)-(2n,n,) combinatorial design, a t-wise uniform set of permutations on n objects and a (2t + 1)-wise uniform set of permutations on n objects. Using the complete design in this procedure gives a t-wise uniform set of permutations on n objects whose size is at most t(2n), the first non-trivial construction of an infinite family of t-wise uniform sets for t4. If a non-trivial design with suitable parameters is found, it will imply a corresponding improvement in the construction. (c) 2013 Wiley Periodicals, Inc. Random Struct. Alg., 46, 531-540, 2015