The maximum number of points on a curve of genus 4 over F₈ is 25

2002/01/23 by David Savitt, Kristin Lauter, Savitt, David +1
Computer Science · Mathematics · #11G20 #14H25 #Algebraic Geometry and Number Theory #Computational Geometry and Mesh Generation #FOS: Mathematics #Mathematical Approximation and Integration #Number Theory (math.NT) #math.NT #msc:11G20 #msc:14H25

paper · pdf · doi:10.48550/arxiv.math/0201226

16 pages, 5 page appendix; replaced July 7, 2002. Paper by David Savitt with an Appendix by Kristin Lauter. Includes a collection of examples by David Savitt that will not be included in the print version of the paper

openalex publication_date 2002/01/23 · arxiv created 2002/07/07 · arxiv updated 2009/11/30 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

This paper proves that the maximum number of rational points on a smooth, absolutely irreducible genus 4 curve over the field of 8 elements is 25. The body of the paper shows that 27 points is not possible using techniques from algebraic geometry. The appendix shows that 26 points is not possible by examining the zeta functions.

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