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: 2024-09-05.
http://mint.sbg.ac.at/desc_FSemirat.html