Let $m$ be a positive integer and $q$ be a prime power. For large finite base fields $\mathbb F_q$, we show that any curve can be used to produce a complete $m$-arc as long as some generic explicit geometric conditions on the curve are verified. To show the effectiveness of our theory, we derive complete $m$-arcs from hyperelliptic curves and from Artin-Schreier curves.

翻译：设$m$为正整数，$q$为素数的幂。对于大有限基域$\mathbb F_q$，我们证明：只要曲线满足某些显式的一般几何条件，任意曲线均可用于生成完全$m$-弧。为展示该理论的有效性，我们从超椭圆曲线和Artin-Schreier曲线出发，推导出完全$m$-弧。