  We describe an implementation of a computer search for the "small" excluded
minors for a class of matroids representable over a partial field. Using these
techniques, we enumerate the excluded minors on at most 15 elements for both
the class of dyadic matroids, and the class of 2-regular matroids. We
conjecture that there are no other excluded minors for the class of 2-regular
matroids; whereas, on the other hand, we show that there is a 16-element
excluded minor for the class of dyadic matroids.
