The maximum number of points on a curve of genus 4 over F_8 is 25
Abstract
Description
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.
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
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