The finite-range 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 finite-range upper-bound conjecture. In $PG(2,q)$,

$$t_{2}(2,q)<5\sqrt{q}\quad \text{for }q\leq 8192.$$

This conjecture gives a uniform numerical bound over the specified finite range of plane orders, extending the computational estimates discussed in the source. The supplied source gives no evidence that it has been resolved.