Hurlbert–Mykkeltveit–Parker conjecture on de Bruijn arrays

An $(r,v;n,m)_d$-array is an array over a $d$-symbol alphabet in which every $n\times m$ window appears exactly once; when the array is a torus, windows wrap around the boundaries. The parameters $r$ and $v$ denote the array dimensions.

Hurlbert–Mykkeltveit–Parker conjecture. There exists an $(r,v;n,m)_d$-array whenever

$$rv=d^{nm}$$

if and only if the array is a torus, $r>n$ or $r=n=1$, and $v>m$ or $v=m=1$.

These conditions are conjectured to be sufficient in addition to the necessary conditions for de Bruijn arrays discussed in the paper. The source provides no resolution status for this conjecture.