manYPoints – Table of Curves with Many Points
Entry details for q = 591 = 59, g = 4
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Lower bound Nmin = 116

Submitted by Everett Howe
Date 08-30-2011
Reference Everett W. Howe
New bounds on the maximum number of points on genus-4 curves over small finite fields
Arithmetic, Geometry, Cryptography and Coding Theory (Y. Aubry, C. Ritzenthaler, and A. Zykin, eds.), Contemporary Mathematics 574, American Mathematical Society, Providence, RI, 2012, pp. 69–86
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Here is a genus-4 curve with 116 points: y^2 = x^3 + 2*x + 22, z^2 = 2*x^3 + x^2 - x + 9
Tags Explicit curves

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Upper bound Nmax = 118

Submitted by Everett Howe
Date 06-17-2010
Reference Alexey Zaytsev
Optimal curves of low genus over finite fields
Finite Fields Appl. 37 (2016), 203–224
Comments
Tags Analysis of Hermitian forms

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