Construction for Strength k = 1
For all b, m ≥ 1, and s, the multiset consisting of the points (n/b,…, n/b) ∈ [0, 1)s for n = 0,…, b−1 each with multiplicity bm−1 is a (m−1, m, s) = (t, t + 1, s)-net in base b.
A digital net over Fb can be obtained by using any set of s m×m-matrices over Fb, given that non of the first row vectors of the generator matrices is the zero vector.
See Also
Construction 5 in [1].
References
| [1] | Gary L. Mullen, Arijit Mahalanabis, and Harald Niederreiter. Tables of (t, m, s)-net and (t, s)-sequence parameters. In Harald Niederreiter and Peter Jau-Shyong Shiue, editors, Monte Carlo and Quasi-Monte Carlo Methods in Scientific Computing, volume 106 of Lecture Notes in Statistics, pages 58–86. Springer-Verlag, 1995. |
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. “Construction for Strength k = 1.”
From MinT—the database of optimal net, code, OA, and OOA parameters.
Version: 2024-09-05.
http://mint.sbg.ac.at/desc_NK1.html