manYPoints – Table of Curves with Many Points
Entry details for q = 72 = 49, g = 4
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Lower bound Nmin = 102

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
Comments
Here is a genus-4 curve with 102 points: y^2 = x^3 + x, z^2 = x^3 + x^2 + x + 4
Tags Explicit curves

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Upper bound Nmax = 105

Submitted by Momonari KUDO
Date 07-13-2016
Reference Momonari Kudo, Shushi Harashita
Superspecial curves of genus $4$ in small characteristic
Finite Fields Appl. 45 (2017), 131–169
Comments
See Theorem B of Section 1 (or Section 5.1).
Tags None

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