  We study the singularity probability of random integer matrices. Concretely,
the probability that a random $n \times n$ matrix, with integer entries chosen
uniformly from $\{-m,\ldots,m\}$, is singular. This problem has been well
studied in two regimes: large $n$ and constant $m$; or large $m$ and constant
$n$. In this paper, we extend previous techniques to handle the regime where
both $n,m$ are large. We show that the probability that such a matrix is
singular is $m^{-cn}$ for some absolute constant $c>0$. We also provide some
connections of our result to coding theory.
