  A net in $\mathbb{P}^2$ is a configuration of lines $\mathcal A$ and points
$X$ satisfying certain incidence properties. Nets appear in a variety of
settings, ranging from quasigroups to combinatorial design to classification of
Kac-Moody algebras to cohomology jump loci of hyperplane arrangements. For a
matroid $M$ and rank $r$, we associate a monomial ideal (a monomial variant of
the Orlik-Solomon ideal) to the set of flats of $M$ of rank $\le r$. In the
context of line arrangements in $\mathbb{P}^2$, applying Alexander duality to
the resulting ideal yields insight into the combinatorial structure of nets.
