manYPoints – Table of Curves with Many Points
Entry details for q = 27 = 128, g = 5
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Lower bound Nmin = 232

Submitted by Everett Howe
Date 05-20-2020
Reference Not available
Comments
Let r be an element of F_128 that satisfies r^7 + r + 1 = 0. Then the curve C over F_128 defined by the two equations
y^2 + y = r^19*x + (r^104*x + r^78)/(x^2 + x + 1)
z^2 + z = r^19*x + (r^104*x + r^61)/(x^2 + x + 1) + 1
has genus 5 and has 232 rational points.
Tags Explicit curves, Fibre products of Artin-Schreier curves

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Upper bound Nmax = 234

Submitted by Gerrit Oomens
Date 01-01-1900
Reference O. Moreno, D. Zinoviev, V. Zinoviev
On several new projective curves over F_2 of genus 3, 4 and 5
IEEE Trans. Info. Th. 41 (1995), p. 1643-1645.
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Tags None

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