manYPoints – Table of Curves with Many Points
Entry details for q = 22 = 4, g = 11
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Lower bound Nmin = 26

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 Fibre products of Artin-Schreier curves

User comments

Explicit Curve     
S.E.Fischer
12-19-2014 03:54
We can assume such a curve C as an extension E of degree 2 of the Klein curve K as follows:
K:= y^4 + (x^2 + x + 1)*y^2 + (x^2 + x)*y + x^4 + x^2 +1 ;
E/K := z^2*(x^2 +x ) + z*x^3 + x^2 +x + y^2 +y .
Upper bound Nmax = 29

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.
Comments
A real Weil polynomial we don't know how to eliminate: (x - 1) * (x + 1)^2 * (x + 2)^4 * (x + 3) * (x + 4)^3
Tags None

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