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 Niederreiter, Harald; Xing, Chaoping
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
Notes by Fernando Q. Gouvêa of lectures at Harvard University, 1985.
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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