Algebraic curves with many points over the binary field

For an algebraic curve X over the finite field Fq, we denote by N(X) and g(X) the number of Fq-rational points and genus of X, respectively. Define the asymptotic quantity A(q) by lim supg(X)→∞N(X)/g(X). In this paper, we show an improvement on the best known lower bound on A(2).