The shortest common superpattern conjecture

Let $n(l,m)$ be the length of the shortest word containing every pattern of length $m$ on at most $l$ letters. In the conjecture below, $l$ is a positive integer.

Shortest common superpattern conjecture. For any $l\ge 1$,

$$n(l,l)=l^2-l+1.$$

This would show that the previously stated upper bound $n(l,m)\le l(m-1)+1$ is sharp when $m=l$. The source says that the matching lower bound is apparent in this case but that it has not been proved.