A recursive construction of t ‐wise uniform permutations

We present a recursive construction of a (2 t + 1)‐wise uniform set of permutations on 2 n objects using a ( 2 t + 1 ) − ( 2 n , n , · ) combinatorial design, a t ‐wise uniform set of permutations on n objects and a (2 t + 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 2 n , the first non‐trivial construction of an infinite family of t ‐wise uniform sets for t ≥ 4 . If a non‐trivial design with suitable parameters is found, it will imply a corresponding improvement in the construction. © 2013 Wiley Periodicals, Inc. Random Struct. Alg., 46, 531–540, 2015