There Is No Drake/Larson Linear Space on 30 Points

摘要

A linear space is Drake/Larson if it contains at least two lines and there are no lines of size 2, 3 or 6. The existence or nonexistence of such linear spaces on v points is known except for v = 30. The purpose of this article is to settle the remaining case on thirty points in the negative. This result relies on a combination of parameter calculation and exhaustive computer search.