Entry details for q = 22 = 4, g = 8
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Lower bound Nmin = 21

Submitted by Gerrit Oomens
Date 01/01/1900
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.
Tags Methods from general class field theory

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Upper bound Nmax = 24

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.
The Oesterlé bound. Here is a real Weil polynomial that we don't know how to eliminate: x * (x + 2)^4 * (x + 3) * (x + 4)^2
Tags Oesterlé bound

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Restrictions on curve     
Everett Howe
05/04/2010 00:36
In fact, the real Weil polynomial listed above is the *only* possibility for a curve with 24 points. Also, if there is a curve with this real Weil polynomial, it must have a degree-3 map to the unique elliptic curve with 8 points.

All this can be deduced from the Magma package IsogenyClasses.magma, found at http://alumnus.caltech.edu/~however/Magma/IsogenyClasses.magma