manYPoints – Table of Curves with Many Points
Entry details for q = 51 = 5, g = 13
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Lower bound Nmin = 36

Submitted by C. Ritzenthaler
Date 10-16-2009
Reference Harald Niederreiter, Chaoping Xing
Global function fields with many rational places over the quinary field
Demonstratio Math. 30 (1997), no. 4, 919--930
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Tags Methods from general class field theory

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Upper bound Nmax = 40

Submitted by Everett Howe
Date 04-14-2010
Reference Jean-Pierre Serre
Rational points on curves over finite fields. With contributions by Everett Howe, Joseph Oesterlé and Christophe Ritzenthaler. Edited by Alp Bassa, Elisa Lorenzo García, Christophe Ritzenthaler and René Schoof
Documents Mathématiques 18, Société Mathématique de France, Paris, 2020
Comments
The Oesterlé bound. Here is a real Weil polynomial that we don't know how to eliminate: (x + 2)^4 * (x + 4)^3 * (x^2 + 2*x - 2) * (x^2 + 6*x + 7)^2
Tags Oesterlé bound

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