A subset of \({\mathbb {F}}_q^2\) is called an arc if it does not contain three collinear points. We show that there are at most \(\left( {\begin{subarray}{c}(1 + o(1))q\\ m\end{subarray}}\right) \) arcs of size \(m \gg q^{1/2} (\log q)^{3/2}\) , nearly matching a trivial lower bound of \(\left( {\begin{subarray}{c}q\\ m\end{subarray}}\right) \) . This was previously known to hold for \(m \gg q^{2/3} (\log q)^3\) , by a result of Bhowmick and Roche-Newton. The lower bound on m is best possible up to a logarithmic factor.
