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arXiv · 2609.11679

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

Peter Beelen·Maria Montanucci·Jonathan Niemann
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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.

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Peter Beelen, Maria Montanucci, Jonathan Niemann. 2026-09-10. A maximal function field of genus $17$ over $\mathbb{F}_{11^2}$. https://arxiv.org/abs/2609.11679

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