Entry details for q = 33 = 27, g = 9
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Lower bound Nmin = 100

Submitted by Everett Howe
Date 06-12-2023
Reference Not available
Comments
Let
f1 := x^3 + 2*x;
f2 := x^4 + 2*x + 2;
f3 := x^4 + x^3 + 2;

Then the curve defined by
y^2 = f1*f2
z^2 = f1*f3

has genus 9 and has 100 points.

This example was found by searching through curves of the given form.
Tags Analysis and enumeration, Towers of curves with many points

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Upper bound Nmax = 113

Submitted by Everett Howe
Date 04-14-2010
Reference E. W. Howe, K. E. Lauter
Improved upper bounds for the number of points on curves over finite fields
Ann. Inst. Fourier (Grenoble) 53 (2003) 1677–1737.
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