A tower with non-Galois steps which attains the Drinfeld-Vladut bound
A tower \(F_1\subseteq F_2\subseteq\ldots\) of algebraic function fields \({F_i}| {\mathbb F_q}\) is said to be asymptotically optimal if \(\text{ lim}_{i\to\infty} F_i(\mathbb F_q)/g_i(F_i)\) is equal to the Drinfeld-Vladut bound \(\sqrt{q}-1\). For \(q\) a square, several of such towers were explicitly constructed by \textit{A. Garcia} and \textit{H. Stichtenoth} [see Invent. Math. 121, 211--222 (1995; Zbl 0822.11078) and J. Number Theory 61, 248--273 (1996; Zbl 0893.11047)]. A property of these towers is that each step \(F_{i+1}| F_i\) is Galois. In this paper, for \(q>4\), the authors construct an asymptotically optimal tower with non-Galois steps.
scientific article; zbMATH DE number 2081176