Entry details for q = 31 = 3, g = 9
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Lower bound Nmin = 19

Submitted by Gerrit Oomens
Date 01/01/1900
Reference G. van der Geer, M. van der Vlugt
How to construct curves over finite fields with many points
In: Arithmetic Geometry, (Cortona 1994), F. Catanese Ed., Cambridge Univ. Press, Cambridge, 1997, p. 169-189.
Comments
Tags Fibre products of Artin-Schreier curves

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Defining equation     
Isabel Pirsic
06/08/2012 16:31
y^9 + (2*x^6 + 2*x^4 + 2*x^2 + 2)*y^3 + (x^6 + x^4 + x^2)*y + 2*x^12 + 2*x^9 + 2*x^8 + x^7 + 2*x^6 + x^5 + 2*x^4

Reference:
H. Niederreiter, C. P. Xing Cyclotomic function fields, Hilbert class fields and global function fields with many rational places
Acta Arithm. 79 (1997), p. 59-76.
Upper bound Nmax = 19

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)^2 * (x^2 + 4*x + 2)^2 * (x^3 + 3*x^2 - 2*x - 5)
Tags Oesterlé bound

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