Entry details for q = 25 = 32, g = 6
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Lower bound Nmin = 89

Submitted by Everett Howe
Date 12/08/2019
Reference Not available
Comments
An explicit example is given by

y^2 + y = r^7 *x + r^21/(x^2 + x + 1) + 1
z^2 + z = r^14 *x + r^11/(x^2 + x + 1) + 1

where r satisfies r^5 + r^2 + 1 = 0.
Tags Explicit curves, Fibre products of Artin-Schreier curves

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Upper bound Nmax = 96

Submitted by Everett Howe
Date 04/14/2010
Reference E. W. Howe and K. E. Lauter
Improved upper bounds for the number of points on curves over finite fields
Ann. Inst. Fourier (Grenoble) 53 (2003) 1677–1737.
Comments
A real Weil polynomial we don't know how to eliminate: (x + 8) * (x + 11)^5
Tags None

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