A New Tower over Cubic Finite Fields

We present a new explicit tower of function fields $(F_n)_{n\ge0}$ over the finite field with $l=q^3$ elements, where the limit of the ratios (number of rational places of $F_n$)/(genus of $F_n$) is bigger or equal to $2(q^2-1)/(q+2)$. This tower contains as a subtower the tower which was introduced by Bezerra–Garcia–Stichtenoth, and in the particular case $q=2$ it coincides with the tower of van der Geer–van der Vlugt. Many features of the new tower are very similar to those of the optimal wild tower in an earlier work by the second and the third author over the quadratic field $\mathbf F_q^2$ (whose modularity was shown by Elkies).