Entry details for q = 24 = 16, g = 8
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Lower bound Nmin = 63

Submitted by Karl Rökaeus
Date 06-29-2011
Reference Karl Rökaeus
Computer search for curves with many points among abelian covers of genus 2 curves
arXiv:1106.5176v1 [math.NT]
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Tags Methods from general class field theory

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Upper bound Nmax = 75

Submitted by Gerrit Oomens
Date 01-01-1900
Reference Bradley W. Brock
Private communication, 2004
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Tags None

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explanation     
Everett Howe
11-03-2021 23:47
The Ihara bound says that a genus-8 curve over F_16 has at most 76 points. The only real Weil polynomial consistent with this is (x+7)^5 * (x+8)^3, and this possibility is eliminated by Serre's "resultant 1" method.