Classification of line-transitive point-imprimitive linear spaces with line size at most 12

Abstract

In this paper we complete a classification of finite linear spaces $${\mathcal{S}}$$ with line size at most 12 admitting a line-transitive point-imprimitive subgroup of automorphisms. The examples are the Desarguesian projective planes of orders 4, 7, 9 and 11, two designs on 91 points with line size 6, and 467 designs on 729 points with line size 8.