Archdeacon's existence conjecture for integer Heffter arrays

Let $m,n,s,k$ be integers such that $3\leqslant s\leqslant n$, $3\leqslant k\leqslant m$, and $ms=nk$. An integer Heffter array $\mathrm{H}(m,n;s,k)$ is an $m\times n$ partially filled array with $s$ filled cells in each row and $k$ filled cells in each column, whose entries use one representative from each pair $\{x,-x\}$ partitioning $\{1,2,\ldots,2nk+1\}$, and whose rows and columns each sum to zero.

Archdeacon's conjecture. There exists an integer Heffter array $\mathrm{H}(m,n;s,k)$ if and only if

$$nk\equiv 0,3\pmod 4.$$

This conjecture gives the expected necessary and sufficient arithmetic condition for the existence of integer Heffter arrays with at least three filled cells in every row and column. The source presents it as an established conjecture in the literature; its resolution is not specified here.