Entry details for q = 23 = 8, g = 6
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Lower bound Nmin = 33

Submitted by Gerrit Oomens
Date 01/01/1900
Reference H. Stichtenoth
Algebraic-geometric codes associated to Artin-Schreier extensions of F_q(z)
In: Proc. 2nd Int. Workshop on Alg. and Comb. Coding Theory, Leningrad (1990), p. 203-206.
Tags Fibre products of Artin-Schreier curves

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Explicit example     
Everett Howe
12/08/2019 01:28
Here is an example of a genus-6 curve over F_8 with 33 points:

y^2 + y = x^5 + x^3
z^2 + z = r*x^5 + r^2*x^3

(Here r is an element of F_8 satisfying r^3 + r + 1 = 0.)
Upper bound Nmax = 35

Submitted by Everett Howe
Date 04/14/2010
Reference Kristin Lauter
Geometric methods for improving the upper bounds on the number of rational points on algebraic curves over finite fields
J. Algebraic Geom. 10 (2001) 19–36
See Theorem 3 of Section 5.
Tags None

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