Trace Code for Nets
Every (digital) (t, m, s)-net in base bu with u ≥ 1 yields a (digital) (tʹ, um, us)-net in base b with
tʹ = (u−1)m + t.
In other words, the new net has the same strength as the original net.
For digital nets the result is due to [1, Theorem 9], for general nets to [2, Propagation Rule 7].
See Also
References
| [1] | Harald Niederreiter and Chaoping Xing. Nets, (t, s)-sequences, and algebraic geometry. In Peter Hellekalek and Gerhard Larcher, editors, Random and Quasi-Random Point Sets, volume 138 of Lecture Notes in Statistics, pages 267–302. Springer-Verlag, 1998. |
| [2] | Harald Niederreiter. Constructions of (t, m, s)-nets. In Harald Niederreiter and Jerome Spanier, editors, Monte Carlo and Quasi-Monte Carlo Methods 1998, pages 70–85. Springer-Verlag, 2000. |
| [3] | Harald Niederreiter. Constructions of (t, m, s)-nets and (t, s)-sequences. Finite Fields and Their Applications, 11(3):578–600, August 2005. doi:10.1016/j.ffa.2005.01.001 MR2158777 (2006c:11090) |
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. “Trace Code for Nets.”
From MinT—the database of optimal net, code, OA, and OOA parameters.
Version: 2024-09-05.
http://mint.sbg.ac.at/desc_NTrace.html