The logarithmic upper-bound conjecture for complete arcs in projective planes

Let $PG(2,q)$ be the projective plane of order $q$, and let $t_{2}(2,q)$ denote the smallest size of a complete arc in $PG(2,q)$. The logarithmic upper-bound conjecture. In $PG(2,q)$,

$$t_{2}(2,q)<\sqrt{q}\ln ^{0.75}q\quad \text{for }q\geq 23.$$

This conjecture proposes an asymptotic upper bound for the smallest complete arc, improving the known general bounds up to logarithmic factors. The supplied source gives no evidence that it has been resolved.