manYPoints – Table of Curves with Many Points
Entry details for q = 711 = 71, g = 4
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Lower bound Nmin = 132

Submitted by Vijay
Date 04-16-2010
Reference Vijaykumar Singh, Gary McGuire
The Intersection of Two Fermat Hypersurfaces in P^3 via Computation of Quotient Curves
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The curve of genus 4 defined by the intersection of two Fermat hyper-surfaces x^2+y^2+z^2+w^2=0 and x^3+y^3+z^3+w^3=0 over GF(71) has 132 rational points and hence has defect 4.
Tags Hasse-Weil-Serre bound

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Upper bound Nmax = 134

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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