  The purpose of this paper is to prove that if $G$ is a transitive permutation
group of degree $n\geq 2$, then $G$ can be generated by $\lfloor
cn/\sqrt{\log{n}}\rfloor$ elements, where $c:=\sqrt{3}/2$. Owing to the
transitive group $D_8\circ D_8$ of degree $8$, this upper bound is best
possible. Our new result improves a 2018 paper by the author, and makes use of
the recent classification of transitive groups of degree $48$.
