Algebraic curves over F2 with many rational points

Abstract A smooth, projective, absolutely irreducible curve of genus 19 over F 2 admitting an infinite S -class field tower is presented. Here S is a set of four F 2 -rational points on the curve. This is shown to imply that A (2) = limsup # X ( F 2 )/ g(X) ≥ 4/(19 − 1) ≈ 0.222. Here the limit is taken over curves X over F 2 of genus g ( X ) → ∞.