Entry details for q = 31 = 3, g = 28
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Lower bound Nmin = 37

Submitted by Gerrit Oomens
Date 01/01/1900
Reference H. Niederreiter, C. P. Xing
Global function fields fields with many rational points over the ternary field
Acta Arithm. 83 (1998), p. 65-86.
Comments
Tags Towers of curves with many points

User comments

Defining equation     
Isabel Pirsic
06/08/2012 17:26
y^18 +
(x^6 + x^4 + x^2 + 1)*y^12 +
(2*x^6 + 2*x^4 + 2*x^2)*y^10 +
(x^12 + x^9 + x^8 + 2*x^7 + x^6 + 2*x^5 + x^4)*y^9 +
(x^12 + 2*x^10 + x^6 + 2*x^2 + 1)*y^6 +
(x^12 + 2*x^10 + 2*x^4 + x^2)*y^4 +
(2*x^18 + 2*x^16 + 2*x^15 + x^14 + x^11 + x^9 + 2*x^7 + x^6 + x^5 + 2*x^4)*y^3 +
(x^12 + 2*x^10 + 2*x^6 + x^4)*y^2 +
(x^18 + x^16 + x^15 + 2*x^14 + 2*x^12 + 2*x^11 + x^9 + 2*x^8 +
2*x^7 + x^6)*y +
2*x^27 + 2*x^22 + x^19 + 2*x^17 + x^13 + 2*x^10 + x^9 + x^8

(reference as above, calculated with Magma)
Upper bound Nmax = 43

Submitted by Everett Howe
Date 04/14/2010
Reference Jean-Pierre Serre
Rational points on curves over finite fields
Notes by Fernando Q. Gouvêa of lectures at Harvard University, 1985.
Comments
The Oesterlé bound
Tags Oesterlé bound

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