manYPoints – Table of Curves with Many Points
Entry details for q = 33 = 27, g = 3
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Lower bound Nmin = 56

Submitted by Gerrit Oomens
Date 01-01-1900
Reference Gerard van der Geer, Marcel van der Vlugt
Tables for the function N_q(g)
Final update, March 19, 1998.
Comments
Tags Towers of curves with many points

User comments

Explicit example     
Everett Howe
05-20-2010 22:23
Examples can also be constructed using the method of Howe/Leprévost/Poonen (Forum Math. 12 (2000) 315–364). For example, the plane quartic
x^4 + y^4 + 1 + r^12*x^2 + r^12*y^2 + r^7*x^2*y^2 = 0
(where r^3 - r + 1 = 0) has 56 points.
Upper bound Nmax = 56

Submitted by Everett Howe
Date 06-11-2010
Reference Kristin Lauter
The Maximum or Minimum Number of Rational Points on Genus Three Curves over Finite Fields
Compositio Mathematica 134 87-111 (2002)
Comments
This upper bound follows from Theorem 2 (p. 89) of the cited reference, because 27 = 5^2 + 2.
Tags None

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