  We study and explicitly construct some families of asymptotically exact
sequences of algebraic function fields. It turns out that these families have
an asymptotical class number widely greater than the general Lachaud -
Martin-Deschamps bounds. We emphasize that we obtain asymptotically exact
sequences of algebraic function fields over any finite field $\F_q$, in
particular when $q$ is not a square and that these sequences are dense towers.
