A net in P^2 is a configuration of lines A and points X satisfying certain incidenceproperties. Nets appear in a variety of settings, ranging from quasigroups to combinatorialdesign to classification of Kac–Moody algebras to cohomology jump loci ofhyperplane 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 ≤ r .In the context of line arrangements in P^2, applying Alexander duality to the resultingideal yields insight into the combinatorial structure of nets.