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


[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 © 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: 2015-09-03.

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