Mathon and van Trung's conjecture on perfect sequence covering arrays

For integers $n$ and $k$, let $g(n,k)$ be the minimum covering multiplicity for a perfect sequence covering array with parameters $(n,k)$. The previously known exceptional values include $k=2$ and, by Mathon's construction, $k=4$. Mathon and van Trung's conjecture. If $k\notin\{2,4\}$, then

$$g(k+2,k)>1.$$

This revised conjecture isolates $k=4$ as the only possible additional value at which Levenshtein's conjecture fails. It is presented here without a resolution status; related computer results establish $g(7,4)>1$, $g(7,5)>1$, and $g(8,6)>1$.