Entry details for q = 34 = 81, g = 3
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Lower bound Nmin = 136

Submitted by Gerrit Oomens
Date 01-01-1900
Reference M. Wirtz
Konstruktion und Tabellen linearer Codes
Westfälische Wilhelms-Universität Münster, 1991.
Comments
Tags Explicit curves

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Explicit curve     
Everett Howe
05-17-2010 23:41
Let r be an element of F_9 that satisfies r^2 = r + 1. Let C be the plane quartic y^3 - r*y = x^4 + x^2. Then the Weil polynomial of C is (t^2 + 9)^3, and C has 136 points over F_{81}.
Upper bound Nmax = 136

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).
Comments
The Hasse-Weil-Serre bound
Tags Hasse-Weil-Serre bound

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