Entry details for q = 192 = 361, g = 3
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Lower bound Nmin = 476

Submitted by C. Ritzenthaler
Date 06/29/2009
Reference Jaap Top
Maximal quartics over F_p^2
Tags Explicit curves

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A hyperelliptic example     
Everett Howe
06/17/2010 17:15
The cited reference gives as an example the plane quartic x^4 + y^4 + z^4 = 0. A paper of Kodama, Top, and Washio ("Maximal hyperelliptic curves of genus three", Finite Fields Appl. 15 (2009) 392–403) points out that the hyperelliptic curve y^2 = x^7 + x provides another example.
Upper bound Nmax = 476

Submitted by Everett Howe
Date 06/10/2010
Reference Jean-Pierre Serre
Sur le nombre de points rationnels d'une courbe algébrique sur un corps fini
C. R. Acad. Sci. Paris Sér. I Math. 296 (1983), 397–402. (= Œuvres III, No. 128, 658–663).
The Hasse-Weil-Serre bound
Tags Hasse-Weil-Serre bound

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