manYPoints – Table of Curves with Many Points
Entry details for q = 32 = 9, g = 5
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Lower bound Nmin = 32

Submitted by Gerrit Oomens
Date 01-01-1900
Reference Gerard van der Geer, Marcel 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 Elliptic modular curves

User comments

Explicit Curve     
S.E.Fischer
02-24-2017 21:47
Another equation is given by
(x^4 + 1)*y^4 + 2*x^3*y^3 + y^2 + 2*x*y + x^4 + x^2 = 0.
Other reference     
C. Ritzenthaler
02-01-2013 10:01
A curve is also constructed in the paper "polynomials with a restricted range and curves with many points" by C.A. Ramos and A.G. Ramos. Let a be a root of x^2+x+2=0. Then

y^8=a^2 x^2 (x^2+a^7)

has 32 points over F_9.
Upper bound Nmax = 35

Submitted by Everett Howe
Date 04-14-2010
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
Comments
See Theorem 3 of Section 5.
Tags None

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