Preprint A528/2007
A new tower over cubic finite fields

Henning Stichtenoth | Garcia, Arnaldo | Bassa, Alp

**Keywords: **
finite fields | function fields | tower | limit of tower | Zink?s bound

We present an explicit new tower of function fields F_n for n = 0,1,2,.... over the finite field with 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 over the quadratic field F_{q^2}(whose modularity was shown by Elkies).