All-order upper-bound conjecture for complete arcs

Let $t_{2}(2,q)$ be the smallest size of a complete arc in $\mathrm{PG}(2,q)$, and let the bounds denoted in the source by

$$through$$

be the explicit upper bounds obtained from the computed complete arcs and lexiarcs. All-order upper-bound conjecture. These bounds hold for every prime power $q\geq109$. The bounds are proved computationally for all prime powers through $301813$, with additional sporadic computations up to $430007$; the conjecture extrapolates their validity to all prime powers $q\geq109$.