  We prove the following result which was conjectured by Stichtenoth and Xing:
let $g$ be the genus of a projective, irreducible non-singular curve over the
finite field $\Bbb F_{q^2}$ and whose number of $\Bbb F_{q^2}$-rational points
attains the Hasse-Weil bound; then either $4g\le (q-1)^2$ or $2g=(q-1)q$.
