  A projective, smooth, absolutely irreducible algebraic curve X of genus g
defined over a finite field F_q is called optimal if for every other such genus
g curve Y over F_q one has $\#Y(F_q)\le \#X(F_q)$. In this paper we show that
for $g\le 5$ there is a unique optimal genus g curve over F_2. For g=6 there
are precisely two and for g=7 there are at least two.
