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arXiv · 1609.01838

Curves of medium genus with many points

Everett W. Howe
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Abstract

The defect of a curve over a finite field is the difference between the number of rational points on the curve and the Weil-Serre upper bound for the number of points on the curve. We present algorithms for constructing curves of genus 5, 6, and 7 with small defect. Our aim is to be able to produce, in a reasonable amount of time, curves that can be used to populate the online table of curves with many points found at http://www.manypoints.org.

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Everett W. Howe. 2016-09-07. Curves of medium genus with many points. https://doi.org/10.1016/j.ffa.2017.06.006

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