  We show that under reasonable conditions, a random $n\times (2+\epsilon) n$
integer matrix is surjective on $\mathbb{Z}^{n}$ with probability
$1-O(e^{-cn})$. We also conjecture that this should hold for $n\times
(1+\epsilon)n$, and provide a counterexample to show that our "reasonableness"
conditions are necessary.
