Families of curves over any finite field with a class number greater than the Lachaud - Martin-Deschamps bounds

Abstract

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.