The existence conjecture for universal cycles of multisets

Let $[n]=\{1,\ldots,n\}$, and let a Universal Cycle for $t$-multisets of $[n]$ be a cyclic sequence of $\binom{n+t-1}{t}$ integers from $[n]$ in which every $t$-multiset of $[n]$ appears exactly once consecutively. Universal-cycle existence conjecture. For $t$ large enough in terms of $n$, Universal Cycles for $t$-multisets of $[n]$ exist if and only if

$$n\mid\binom{n+t-1}{t}.$$

The divisibility condition is necessary because each symbol must occur equally often in the cyclic sequence. The paper proves the conjecture completely for $t\in\{2,3\}$ and partially for $t\in\{4,6\}$, while the general case remains open.