A recursive construction of t‐wise uniform permutations. Issue 3 (7th August 2013) - Finucane, Hilary
Abstract 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 t2n, 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