Entry details for q = 24 = 16, g = 3
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Lower bound Nmin = 38

Submitted by Gerrit Oomens
Date 01/01/1900
Reference J-P. Serre
Quel est le nombre maximum de points rationnels que peut avoir une courbe algébrique de genre g sur un corps fini F_q?
Résumé des Cours de 1983-1984 (=Oeuvres III, No. 132, p. 701-705).
Tags Explicit curves

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Explicit example     
Everett Howe
05/20/2010 22:06
In his Harvard notes, Serre gives an explicit example (which appears with a small misprint): The biquadratic extension of F_16(x) defined by
y^2 + y = x + r/x
z^2 + z = x + r/(x+1)
where r satisfies r^2 + r + 1 = 0.
Upper bound Nmax = 38

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. 2 of Sec. 4 of the cited reference.
Tags None

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