  In 1991, Weidong Fang and Huiling Li proved that there are only finitely many
non-trivial linear spaces that admit a line-transitive, point-imprimitive group
action, for a given value of gcd(k,r), where k is the line size and r is the
number of lines on a point. The aim of this paper is to make that result
effective. We obtain a classification of all linear spaces with this property
having gcd(k,r) at most 8. To achieve this we collect together existing theory,
and prove additional theoretical restrictions of both a combinatorial and group
theoretic nature. These are organised into a series of algorithms that, for
gcd(k,r) up to a given maximum value, return a list of candidate parameter
values and candidate groups. We examine in detail each of the possibilities
returned by these algorithms for gcd(k,r) at most 8, and complete the
classification in this case.
