Entry details for q = 21 = 2, g = 10
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Lower bound Nmin = 13

Submitted by Gerrit Oomens
Date 01/01/1900
Reference J-P. Serre
Letter to G. van der Geer
September 1, 1997.
Comments
Tags Methods from general class field theory

User comments

Correction     
S.E.Fischer
12/20/2014 03:39
The extension E/F leads to a curve of genus 4 with 8 points. Extending once again by H of degree 2 leads to the desired result, as we write
H/(E/F):= v^2 + v*x + x^3 + x .
Explicit Curve     
S.E.Fischer
12/18/2014 15:27
We can assume such a curve C as an extension E of degree 2 of a curve F of genus 1 as follows:
F:= (x + y + x*y) * x*y + x + 1
E/F := z^2 * x + z + x^2 * y^2
My reference corrected     
Isabel Pirsic
06/19/2012 16:18
G. van der Geer
Hunting for curves over finite fields with many points
arXiv:0902.3882
Defining equation     
Isabel Pirsic
06/19/2012 14:17
y^8 +
(x^4 + x + 1)*y^4 +
(x^2 + x)*y^2 +
(x^4 + x^2)*y +
(x^12 + x^4)

Ref: G. van der Geer, M. van der Vlugt
How to construct curves over finite fields with many points
In: Arithmetic Geometry, (Cortona 1994), F. Catanese Ed.,
Cambridge Univ. Press, Cambridge, 1997, p. 169-189.
Upper bound Nmax = 13

Submitted by Gerrit Oomens
Date 01/01/1900
Reference J-P. Serre
Letter to G. van der Geer
September 1, 1997.
Comments
Tags None

User comments

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