Chung–Diaconis–Graham conjecture on universal cycles

Let $[n]=\{1,\dots,n\}$, and let $\binom{[n]}{k}$ be the family of all $k$-subsets of $[n]$. A universal cycle for $\binom{[n]}{k}$ is a cyclic sequence of length $\binom{n}{k}$ whose every $k$ consecutive elements are distinct and whose consecutive $k$-element sets are precisely the members of $\binom{[n]}{k}$, each exactly once. The necessary divisibility condition is $k\mid\binom{n-1}{k-1}$.

Chung–Diaconis–Graham conjecture. For every $k\in\mathbb{N}$, there exists $n_0\in\mathbb{N}$ such that for all $n\ge n_0$, there exists a universal cycle for $\binom{[n]}{k}$ whenever $k$ divides $\binom{n-1}{k-1}$.

This conjecture asserts that the evident divisibility condition is asymptotically sufficient for universal cycles. The paper proves the claim in the complete-hypergraph case, thereby confirming the conjecture.