manYPoints – Table of Curves with Many Points
Entry details for q = 31 = 3, g = 6
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Lower bound Nmin = 14

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 Towers of curves with many points

User comments

Defining equation     
Isabel Pirsic
06-08-2012 16:10
y^6 + x^2*y^4 + (x^4 + 2*x^3 + x^2)*y^3 + x^4*y^2 + (2*x^6 + x^5 + 2*x^4)*y + 2*x^9 + 2*x^8 + x^7 + x^6

(Reference as above)
Upper bound Nmax = 14

Submitted by Everett Howe
Date 04-14-2010
Reference E. W. Howe, 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 + 2)^2 * (x + 3) * (x^3 + 3*x^2 - 3*x - 6)
Tags None

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