Mayhew–Newman–Welsh–Whittle conjecture on sparse paving matroid minors

A matroid is sparse paving if its nonspanning circuits are hyperplanes; equivalently, no nonbasis of size equal to the rank can be transformed into another nonbasis by exchanging one element for another. Let $N$ be a sparse paving matroid, and let $E$ be a ground set. Mayhew–Newman–Welsh–Whittle conjecture. Almost every matroid has an $N$-minor; that is, the fraction of matroids on ground set $E$ that do not have an $N$-minor tends to $0$ as $|E|\to\infty$. This conjecture asserts that every fixed sparse paving matroid occurs as a minor in almost every matroid, strengthening the broader belief that almost every matroid is sparse paving. Its resolution is not indicated in the source.