  This paper continues previous work, based on systematic use of a formula of
L. Scott, to detect Hurwitz groups. It closes the problem of determining the
finite simple groups contained in $PGL_n(F)$ for $n\leq 7$ which are Hurwitz,
where $F$ is an algebraically closed field. For the groups $G_2(q)$, $q\geq 5$,
and the Janko groups $J_1$ and $J_2$ it provides explicit $(2,3,7)$-generators.
