manYPoints – Table of Curves with Many Points
Entry details for q = 22 = 4, g = 8
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Lower bound Nmin = 22

Submitted by Everett Howe
Date 04-20-2020
Reference Everett W. Howe
The maximum number of points on a curve of genus eight over the field of four elements
J. Number Theory 220 (2021) 320–329
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An example is given by
y^2 + (x^3 + x + 1)y = x^6 + x^5 + x^4 + x^2
z^3 = (x+1)y + x^2

This is a degree-3 Kummer extension of the genus-2 curve defined by the first equation, ramified at 4 points.
Tags Explicit curves

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Upper bound Nmax = 24

Submitted by Gerrit Oomens
Date 01-01-1900
Reference H. Niederreiter, C. P. Xing
Cyclotomic function fields, Hilbert class fields and global function fields with many rational places
Acta Arithm. 79 (1997), p. 59-76.
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Tags None

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