A maximal function field of genus $17$ over ${\mathbb{F}}_{11^2}$

Abstract

In this article, we describe a new maximal function field $G$ over the finite field ${\mathbb{F}}_{11^2}$ with $11^2$ elements and show that it cannot be obtained as a subfield of the Hermitian function field. This provides the first known ${\mathbb{F}}_{p^2}$-maximal function field that satisfies this property. Further, we compute the automorphism group of $G$. The new maximal function field was found using AI.