Entry details for q = 131 = 13, g = 4
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Lower bound Nmin = 38

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
Here is a genus-4 curve with 38 points: y^2 = x^3 + 4, z^2 = x^3 + x^2 - 4*x - 3
Tags Explicit curves

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Explicit Curve     
02/24/2017 21:40
Another equation is given by
(x^4 + 7)*y^4 + x^3*y^3 + 5*x*y + 7*x^4 = 0.
Upper bound Nmax = 39

Submitted by Everett Howe
Date 04/14/2010
Reference Everett W. Howe, Kristin E. Lauter
New methods for bounding the number of points on curves over finite fields
Geometry and Arithmetic (C. Faber, G. Farkas, and R. de Jong, eds.), European Mathematical Society, 2012, pp. 173–212
A real Weil polynomial we don't know how to eliminate: (x + 4) * (x + 7)^3
Tags None

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