On Universal Cycles for k-Subsets of an n-Set

A universal cycle, or Ucycle, for k-subsets of [n] = {1,...,n} is a cyclic sequence of $(\stackerel{n}{k})$ integers with the property that each subset of [n] of size k appears exactly once consecutively in the sequence. Chung, Diaconis, and Graham have conjectured their existence for fixed k and large n when $n|(\stackerel{n}{k})$. Here the Ucycles for k=3, 4, 6, and large n relative prime to k are exhibited.