manYPoints – Table of Curves with Many Points
Entry details for q =
3
3
= 27
, g =
9
Table
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Lower bound
N
min
= 100
Earlier entry
Submitted by
Everett Howe
Date
06-12-2023
Reference
Not available
Comments
Let
f1 := x^3 + 2*x;
f2 := x^4 + 2*x + 2;
f3 := x^4 + x^3 + 2;
Then the curve defined by
y^2 = f1*f2
z^2 = f1*f3
has genus 9 and has 100 points.
This example was found by searching through curves of the given form.
Tags
Analysis and enumeration, Towers of curves with many points
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Upper bound
N
max
= 113
Earlier entry
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 + 5) * (x + 10)^8
Tags
None
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