A logarithmic bound for the irredundant base size of primitive groups

Let $G$ be a finite primitive group of degree $t$. A primitive large-base group is the exceptional family referred to in the preceding results, and let $coperatorname{I}(G)$ denote the irredundant base statistic for $G$.

Logarithmic irredundant-base conjecture. There exists a constant $C>0$ such that, if $G$ is not a primitive large-base group, then

$$\operatorname{I}(G) < C \log t.$$

This conjecture seeks to extend the paper's height bound to the irredundant-base statistic while eliminating the standard-action exceptions in the preceding theorem. Its resolution is not given in the supplied text.