Entry details for q = 31 = 3, g = 7
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Lower bound Nmin = 16

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.
Comments
Tags Drinfeld modules of rank 1

User comments

reference corrected     
Isabel Pirsic
06/15/2012 12:23
The above def. equation was actually from
B. Lopez, I. Luengo
Algebraic curves over F_3 with many rational points
In: Algebra, arithmetic and geometry with applications.

The def.Eq. for Example 3.7 in Niederreiter/Xing's paper is


y^8 +
(2*x^5 + x^4 + x^3 + x^2 + x + 2)*y^7 +
(x^7 + x^6 + x^5 + 2*x^4 + 2*x^3 + x^2 + x + 1)*y^6 +
(x^10 + x^8 + 2*x^3 + 2)*y^5 +
(x^14 + x^12 + x^10 + 2*x^8 + 2*x^7 + x^4 + 2*x^2 + 2*x + 1)*y^4 +
(2*x^15 + 2*x^14 + 2*x^12 + 2*x^11 + 2*x^8 + x^7 + x^6 + x^5 + 2*x^2 + 2*x + 2)*y^3 +
(x^14 + x^12 + x^11 + 2*x^8 + 2*x^3 + 1)*y^2 +
(2*x^11 + x^8 + 2*x^7 + x^5 + 2*x^3 + x^2 + x + 2)*y +
x^4 + x^3 + x^2 + x + 1
Defining equation     
Isabel Pirsic
06/08/2012 18:01
2*x*y^5 +
(2*x^3 + x^2 + 2*x + 1)*y^4 +
(x^4 + x^3 + x + 2)*y^3 +
(2*x^4 + x)*y^2 +
(2*x^5 + x^4 + x^3 + 2*x^2 + 2*x)*y +
2*x^4 + x^3
Upper bound Nmax = 16

Submitted by Everett Howe
Date 04/14/2010
Reference Kristin Lauter
Zeta functions of curves over finite fields with many rational points
pp. 167–174 in: Coding theory, cryptography and related areas (J. Buchmann, T. Høholdt, H. Stichtenoth, H. Tapia-Recillas, eds.), Springer, Berlin 1998
Comments
Tags None

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