## Extracting Embedded OOA

Given a (digital) (*m*−*k*, *m*, *s*)-net N in base *b*, a (linear) ordered orthogonal array A with parameters OOA(*b*^{m}, *s*, *S*_{b}, *T *, *k*) can be constructed for all *T * with *T * ≥ *k*/*s* [1] [2]. If N is digital over **F**_{b}, A is linear and its dual is a linear [(*s*, *T *), *sT *−*m*, *k* + 1]-NRT-code over **F**_{b}.

### Construction

A is formed based on the *T * leading digits in the *b*-adic expansion of the coordinates of the points of N. More formally, A is obtained from N as

*η*

_{i,j}

^{−1}(⌊

*b*

^{j}

*x*

_{i}⌋ mod

*b*))

_{(i, j) ∈ {1,…, s}×{1,…, T}}:

*∈ N}*

**x**with *η*_{i,j} : *S*_{b}↔{0,…, *b* – 1} denoting arbitrary bijections.

### See Also

Special case for orthogonal arrays and codes

For

*T*≥*k*this process can be reversed by net defined by OOA

### References

[1] | Kenneth Mark Lawrence. A combinatorial characterization of ( t, m, s)-nets in base b.Journal of Combinatorial Designs, 4(4):275–293, 1996.doi:10.1002/(SICI)1520-6610(1996)4:4<275::AID-JCD5>3.0.CO;2-C |

[2] | Gary L. Mullen and Wolfgang Ch. Schmid. An equivalence between ( t, m, s)-nets and strongly orthogonal hypercubes.Journal of Combinatorial Theory, Series A, 76(1):164–174, October 1996.doi:10.1006/jcta.1996.0098 |

### 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. “Extracting Embedded OOA.”
From MinT—the database of optimal net, code, OA, and OOA parameters.
Version: 2008-04-04.
http://mint.sbg.ac.at/desc_OFromN.html