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PreprintarXiv licencearXiv

A maximal function field of genus $17$ over 𝔽112

  • 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 𝔽112 with 112 elements and show that it cannot be obtained as a subfield of the Hermitian function field. This provides the first known 𝔽p2-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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Cite

BibTeXRIS
BibTeX
@misc{beelen2026maximal,
  title = {{A maximal function field of genus $17$ over $\mathbbF_11^2$}},
  author = {Peter Beelen and Maria Montanucci and Jonathan Niemann},
  howpublished = {arXiv},
  year = {2026},
  month = sep,
  doi = {10.48550/arxiv.2609.11679},
  eprint = {2609.11679},
  archivePrefix = {arXiv},
  url = {https://arxiv.org/abs/2609.11679},
}
RIS
TY  - UNPB
TI  - A maximal function field of genus $17$ over 𝔽_11^2
AU  - Peter Beelen
AU  - Maria Montanucci
AU  - Jonathan Niemann
PY  - 2026
DA  - 2026/09/10
PB  - arXiv
DO  - 10.48550/arxiv.2609.11679
UR  - https://arxiv.org/abs/2609.11679
AB  - In this article, we describe a new maximal function field G over the finite field 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 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.
ER  -