Algebraic curves with many points over the binary field

Abstract

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