manYPoints – Table of Curves with Many Points
Entry details for q =
3
2
= 9
, g =
8
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Lower bound
N
min
= 42
Submitted by
Gerrit Oomens
Date
01-01-1900
Reference
Gerard van der Geer
Hunting for curves over finite fields with many points
arXiv:0902.3882
Comments
Tags
Methods from general class field theory
User comments
Explicit Curve
S.E.Fischer
02-24-2017 20:52
Another equation is given by
y^8 + 2*x^4*y^4 + x^3*y^3 + 2*x^2*y^2 + 2*x*y + x^8 = 0.
Upper bound
N
max
= 46
Earlier entry
Submitted by
Everett Howe
Date
04-14-2010
Reference
Everett W. Howe, Kristin E. Lauter
New methods for bounding the number of points on curves over finite fields
Geometry and Arithmetic (C. Faber, G. Farkas, and R. de Jong, eds.), European Mathematical Society, 2012, pp. 173–212
Comments
A real Weil polynomial we don't know how to eliminate: (x + 5)^4 * (x + 6) * (x^3 + 10*x^2 + 28*x + 20)
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