Entry details for q = 24 = 16, g = 5
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Lower bound Nmin = 49

Submitted by Gerrit Oomens
Date 01/01/1900
Reference 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.
Comments
Tags Fibre products of Artin-Schreier curves

User comments

Explicit Curve     
S.E.Fischer
12/07/2014 04:13
We can assume such a curve C as an extension C' of degree 2 of a maximal curve M of genus 1 as follows:
M := (x + y + x*y) * (x*y) +1 ;
C'/M := z^2 + z*(x*y^5)+ x^2*y^5 .
Explicit Curve     
S.E.Fischer
12/07/2014 04:10
We can assume such a curve C as an extension C' of degree 2 of a maximal curve of genus 1 as follows:
C' := (x + y + x*y) * (x*y) +1 ;
C/C' := z^2 + z*(x*y^5)+ x^2*y^5 .
Upper bound Nmax = 53

Submitted by Everett Howe
Date 04/14/2010
Reference E. W. Howe and 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 + 4) * (x + 8)^4
Tags None

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