A recursive construction of t‐wise uniform permutations. Issue 3 (7th August 2013) - Finucane, Hilary; Peled, Ron; Yaari, Yariv
Abstract We present a recursive construction of a (2t + 1)‐wise uniform set of permutations on 2n objects using a <alternatives><inline-graphic mimetype="image" xlink:href="ark:/27927/pgjb82d3p3" xlink:type="simple" xmlns:xlink="http://www.w3.org/1999/xlink" />(2t+1)−(2n, n, ·)</alternatives> 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 <alternatives><inline-graphic mimetype="image" xlink:href="ark:/27927/pgjb82d3r4" xlink:type="simple" xmlns:xlink="http://www.w3.org/1999/xlink" />t≥4</alternatives>. 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