manYPoints – Table of Curves with Many Points
Entry details for q = 31 = 3, g = 5
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Lower bound Nmin = 13

Submitted by Gerrit Oomens
Date 01-01-1900
Reference C. Ritzenthaler
Existence d'une courbe sur F_3 de genre 5 avec 13 points rationnels
Université Paris VII, 2003.
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Tags Explicit curves

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Explicit defining equation     
Isabel Pirsic
06-08-2012 15:59
x^4+x^3*y^3-x^2-x*y^5+y^5+2*y

(Reference as above)
Upper bound Nmax = 13

Submitted by Everett Howe
Date 04-14-2010
Reference Kristin Lauter
Non-existence of a curve over F_3 of genus 5 with 14 rational points
Proc. Amer. Math. Soc. 128 (2000) 369–374.
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