On the affine Sylvester problem

In 2006 Lenchner and Brönnimann [14] showed that in the affine plane, given nn lines, not all parallel and not all passing through a common point, there have to be at least n6 ordinary points. The present paper improves on this result to show that there must be at least 2n−37 ordinary points, except for a single arrangement of 6 lines with one ordinary point.