Function Fields by Sémirat

In [1] Sémirat gives explicit equations for global function fields F/Fb with b = 2, 4, 8, 16, 32, 128 and b = 3, 9, 27, 81.

Non-Rational Places

[2, Example 5.6] states that the function field over F8 with genus g = 7 and N = 34 rational places has also 14 places of degree 2. Similarly, [2, Example 5.7] states that the function field over F9 with genus g = 5 and N = 32 rational places has also 12 places of degree 2.

References

[1]Stéphan Sémirat.
2-extensions with many points, November 2000.
arXiv:math/0011067v1.
[2]Harald Niederreiter and Ferruh Özbudak.
Low-discrepancy sequences using duality and global function fields.
Acta Arithmetica, 130(1):79–97, 2007.

Copyright

Copyright © 2004, 2005, 2006, 2007, 2008, 2009, 2010 by Rudolf Schürer and Wolfgang Ch. Schmid.
Cite this as: Rudolf Schürer and Wolfgang Ch. Schmid. “Function Fields by Sémirat.” From MinT—the database of optimal net, code, OA, and OOA parameters. Version: 2008-04-04. http://mint.sbg.ac.at/desc_FSemirat.html

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