Entry details for q = 25 = 32, g = 3
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Lower bound Nmin = 64

Submitted by Gerrit Oomens
Date 01-01-1900
Reference S. Sémirat
Problèmes de nombres de classes pour les corps de fonctions et applications
Thèse, Université Pierre et Marie Curie, Paris, 2000.
Tags Towers of curves with many points

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Explicit example     
Everett Howe
05-20-2010 22:08
An explicit example is given by the plane quartic
X^2 + X*Y + r^3*Y^2 + Y + r^26
where X = x^2 + x and Y = y^2 + y, and where r^5 + r^2 + 1 = 0.
Upper bound Nmax = 64

Submitted by Everett Howe
Date 06-11-2010
Reference Kristin Lauter
Geometric methods for improving the upper bounds on the number of rational points on algebraic curves over finite fields
J. Algebraic Geom. 10 (2001) 19–36
This upper bound follows from Cor. 1 of Sec. 3 of the cited reference.
Tags None

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