manYPoints – Table of Curves with Many Points
Entry details for q =
7
1
= 7
, g =
6
Table
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Lower bound
N
min
= 28
Earlier entry
Submitted by
Everett Howe
Date
08-13-2016
Reference
Everett W. Howe
Curves of medium genus with many points
Finite Fields Appl. 47 (2017) 145–160
Comments
Explicit curve: y^2 = f1*f2, z^2 = f1*f3, where f1 = x^2 + 4, f2 = x^3 + 2*x^2 + 2, f3 = x^3 + 4*x^2 + 6*x + 1.
Tags
Explicit curves
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Upper bound
N
max
= 32
Earlier entry
Submitted by
Everett Howe
Date
04-14-2010
Reference
Yasutaka Ihara
Some remarks on the number of rational points of algebraic curves
J. Fac. Sci. Univ. Tokyo Sect. IA Math. 28 (1981) 721–724 (1982)
Comments
The Ihara bound. Here is a real Weil polynomial that we don't know how to eliminate: (x + 4)^6
Tags
Ihara bound
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