Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Ternary and Quaternary Curves of Small Fixed Genus and Gonality with
  Many Rational Points   We extend the computations from our previous paper arXiv:2005.07054 to
determine the maximum number of rational points on a curve over $\mathbb{F}_3$
and $\mathbb{F}_4$ with fixed gonality and small genus. We find, for example,
that there is no curve of genus 5 and gonality 6 over a finite field. We
propose two conjectures based on our data. First, an optimal curve of genus $g$
has gonality at most $\lfloor \frac{g+3}{2} \rfloor$. Second, a curve of
gonality $\gamma$ and large genus over $\mathbb{F}_q$ has $\gamma(q+1)$
rational points.

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The categories of this paper are: physics
18
The categories of this paper are: econ
17
The categories of this paper are: q-fin
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The categories of this paper are: gr-qc
27
The categories of this paper are: comp-gas
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The categories of this paper are: supr-con
29
The categories of this paper are: funct-an
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The categories of this paper are: nlin
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The categories of this paper are: bayes-an
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The categories of this paper are: math-ph
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The categories of this paper are: q-bio
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The categories of this paper are: nucl-th
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The categories of this paper are: chem-ph
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The categories of this paper are: hep-th
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The categories of this paper are: chao-dyn
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The categories of this paper are: stat