  In this paper, we make significant progress on a conjecture proposed by Dan
Archdeacon on the existence of integer Heffter arrays $H(m,n;s,k)$ whenever the
necessary conditions hold, that is, $3\leqslant s \leqslant n$, $3\leqslant
k\leqslant m$, $ms=nk$ and $nk\equiv 0,3 \pmod 4$. By constructing integer
Heffter array sets, we prove the conjecture in the affirmative whenever
$k\geqslant 7\cdot \gcd(s,k)$ is odd and $s\neq 3,5,6,10$.
