Yet More Projective Curves over \field{2}

Abstract

All plane curves of degree less than 7 with coefficients in $\field{2}$ are examined for curves with a large number of $\field{q}$ rational points on their smooth model, for $q=2^m, m = 3,4,...,11$. Known lower bounds are improved, and new curves are found meeting or close to Serre's, Lauter's, and Ihara's upper bounds for the maximal number of $\field{q}$ rational points on a curve of genus g.