Line-transitive point-imprimitive linear spaces with Fang-Li parameter gcd(k, r) at most ten

This paper is a further contribution to the classification of linetransitive finite linear spaces. We prove that if ? is a non-trivial finite linear space such that the Fang-Li parameter gcd(k, r) is 9 or 10, and the group G ? Aut(?) is line-transitive and point-imprimitive, then ? is the Desarguesian projective plane PG(2, 9).