## 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 *b*^{m−1} is a (*m*−1, *m*, *s*) = (*t*, *t* + 1, *s*)-net in base *b*.

A digital net over **F**_{b} can be obtained by using any set of *s* *m*×*m*-matrices over **F**_{b}, 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: 2008-04-04.
http://mint.sbg.ac.at/desc_NK1.html