Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: The maximum number of points on a curve of genus eight over the field of
  four elements   The Oesterl\'e bound shows that a curve of genus 8 over the finite field
$\mathbb{F}_4$ can have at most 24 rational points, and Niederreiter and Xing
used class field theory to show that there exists such a curve with 21 points.
We improve both of these results: We show that a genus-8 curve over
$\mathbb{F}_4$ can have at most 23 rational points, and we provide an example
of such a curve with 22 points, namely the curve defined by the two equations
$y^2 + (x^3 + x + 1)y = x^6 + x^5 + x^4 + x^2$ and $z^3 = (x+1)y + x^2.$

17
The categories of this paper are: q-fin
12
The categories of this paper are: nucl-th
18
The categories of this paper are: econ
35
The categories of this paper are: mtrl-th
20
The categories of this paper are: acc-phys
1
The categories of this paper are: cs
0
The categories of this paper are: hep-ph
13
The categories of this paper are: quant-ph
11
The categories of this paper are: hep-lat
15
The categories of this paper are: nucl-ex
4
The categories of this paper are: cond-mat
5
The categories of this paper are: gr-qc
37
The categories of this paper are: supr-con
29
The categories of this paper are: funct-an
19
The categories of this paper are: eess
24
The categories of this paper are: dg-ga