manYPoints – Table of Curves with Many Points
Entry details for q = 191 = 19, g = 4
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Lower bound Nmin = 48

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 48 points: y^2 = x^3 + 8, z^2 = x^3 - 9*x^2 - 5
Tags Explicit curves

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Explicit Curve     
S.E.Fischer
10-31-2019 15:19
Another equation is given by
x^3 + 7*y^3 + y^2*x^2 + x*y + 1 + 5*x^3*y^3 = 0.
Upper bound Nmax = 50

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
Tags Analysis of Hermitian forms

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