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Mathematics of Computation
Mathematics of Computation
ISSN 1088-6842(online) ISSN 0025-5718(print)

 

Tables of curves with many points


Authors: Gerard van der Geer and Marcel van der Vlugt
Journal: Math. Comp. 69 (2000), 797-810
MSC (1991): Primary 11G20, 14G15; Secondary 14H05
Published electronically: August 18, 1999
MathSciNet review: 1654002
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Abstract: These tables record results on curves with many points over finite fields. For relatively small genus ($0\leq g \leq 50$) and $q$ a small power of $2$ or $3$ we give in two tables the best presently known bounds for $N_{q}(g)$, the maximum number of rational points on a smooth absolutely irreducible projective curve of genus $g$ over a field $\mathbb{F}_{q}$ of cardinality $q$. In additional tables we list for a given pair $(g,q)$ the type of construction of the best curve so far, and we give a reference to the literature where such a curve can be found.


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Additional Information

Gerard van der Geer
Affiliation: Faculteit WINS, Universiteit van Amsterdam, Plantage Muidergracht 24, 1018 TV Amsterdam, The Netherlands
Email: geer@wins.uva.nl

Marcel van der Vlugt
Affiliation: Mathematisch Instituut, Rijksuniversiteit te Leiden, Niels Bohrweg 1, 2300 RA Leiden, The Netherlands
Email: vlugt@wi.leidenuniv.nl

DOI: http://dx.doi.org/10.1090/S0025-5718-99-01143-6
PII: S 0025-5718(99)01143-6
Received by editor(s): October 2, 1997
Received by editor(s) in revised form: April 28, 1998
Published electronically: August 18, 1999
Article copyright: © Copyright 2000 American Mathematical Society