Abstract
We explain a naive approach towards the problem of finding genus 3 curves C over any given finite field \( \mathbb{F}_q \) of odd characteristic, with a number of rational points close to the Hasse-Weil-Serre upper bound \( q + 1 + 3\left[ {2\sqrt q } \right] \) . The method turns out to be successful at least in characteristic 3.
It is a pleasure to thank Hendrik Lenstra for his interest in this work, and for his remarks which led to Section 2 of this paper.
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Auer, R., Top, J. (2002). Some Genus 3 Curves with Many Points. In: Fieker, C., Kohel, D.R. (eds) Algorithmic Number Theory. ANTS 2002. Lecture Notes in Computer Science, vol 2369. Springer, Berlin, Heidelberg. https://doi.org/10.1007/3-540-45455-1_13
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DOI: https://doi.org/10.1007/3-540-45455-1_13
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