## OOA from Sequence

Given a (digital) (*t*, *s*)-sequence S in base *b*, (linear) ordered orthogonal arrays A_{T ,k} with parameters OOA(*b*^{t+k}, *s*, *S*_{b}, *T *, *k*) can be constructed for all *T * ≥ 1 and all integers *k* with 0 ≤ *k* ≤ *sT *−*t*.

Theses OOAs are weaker than the (linear) OOA(*b*^{t+k}, *s* + 1, *S*_{b}, *T *, *k*) obtained by net from sequence followed by extracting the embedded OOA from the net, which have one additional factor. However, the OOAs A_{T ,k} discussed here have the additional property that A_{T ,k} ⊂ A_{T ,k+1}. In the linear case A_{T ,k} is a linear subspace of A_{T ,k+1} and A_{T ,k+1}^{⊥} ⊂ A_{T ,k}^{⊥}, which allows e.g. the application of construction X to the NRT-codes A_{T ,k+1}^{⊥} ⊂ A_{T ,k}^{⊥}.

### Construction

The OOA A_{T ,k} is obtained by taking the first *b*^{t+k} runs of S (which gives an OOA(*b*^{t+k}, *s*, *S*_{b},∞, *k*)) and reducing its depth to *T *.

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