manYPoints - Table of Curves with Many Points
http://www.manypoints.org
manYPoints aims at providing an open access up-to-date source for information on curves over finite fields with many pointsLower bound 100 for q=27, g=9
http://www.manypoints.org/Details.aspx?e1=18313
Let
f1 := x^3 + 2*x;
f2 := x^4 + 2*x + 2;
f3 := x^4 + x^3 + 2;
Then the curve defined by
y^2 = f1*f2
z^2 = f1*f3
has genus 9 and has 100 points.
This example was found by searching through curves of the given form.Lower bound 104 for q=27, g=11
http://www.manypoints.org/Details.aspx?e1=18312
Let r be an element of GF(27) with r^3 - r + 1 = 0 and let
f := (x^2 + r*x + 2) * (x^2 + r^9*x + r^3) * (x^2 + r^25*x + 2);
g1 := x^4 + r^9*x^3 + r^17*x^2 + r^16*x + r^17;
g2 := x^4 + r^12*x^3 + r^10*x^2 + r*x + r^23;
Then the curve defined by
y^2 = f*g1
z^2 = f*g2
has genus 11 and has 104 points.
This example was found by searching through curves of the given form.Lower bound 136 for q=9, g=44
http://www.manypoints.org/Details.aspx?e1=18299
Lower bound 289 for q=25, g=44
http://www.manypoints.org/Details.aspx?e1=18300
Lower bound 145 for q=9, g=45
http://www.manypoints.org/Details.aspx?e1=18301
Lower bound 275 for q=25, g=45
http://www.manypoints.org/Details.aspx?e1=18302
Lower bound 306 for q=25, g=46
http://www.manypoints.org/Details.aspx?e1=18303
Lower bound 74 for q=4, g=47
http://www.manypoints.org/Details.aspx?e1=18304
Lower bound 298 for q=25, g=47
http://www.manypoints.org/Details.aspx?e1=18305
Lower bound 302 for q=25, g=48
http://www.manypoints.org/Details.aspx?e1=18306
Lower bound 1058 for q=169, g=48
http://www.manypoints.org/Details.aspx?e1=18307
Lower bound 315 for q=25, g=49
http://www.manypoints.org/Details.aspx?e1=18308
Lower bound 306 for q=25, g=50
http://www.manypoints.org/Details.aspx?e1=18309
Lower bound 506 for q=49, g=50
http://www.manypoints.org/Details.aspx?e1=18310
Lower bound 1750 for q=361, g=50
http://www.manypoints.org/Details.aspx?e1=18311
Lower bound 236 for q=25, g=36
http://www.manypoints.org/Details.aspx?e1=18285
Lower bound 243 for q=25, g=36
http://www.manypoints.org/Details.aspx?e1=18286
Lower bound 1452 for q=361, g=37
http://www.manypoints.org/Details.aspx?e1=18287
Lower bound 131 for q=9, g=38
http://www.manypoints.org/Details.aspx?e1=18288
Lower bound 1224 for q=289, g=38
http://www.manypoints.org/Details.aspx?e1=18289