OOA from Sequence
Given a (digital) (t, s)-sequence S in base b, (linear) ordered orthogonal arrays AT ,k with parameters OOA(bt+k, s, Sb, 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(bt+k, s + 1, Sb, T , k) obtained by net from sequence followed by extracting the embedded OOA from the net, which have one additional factor. However, the OOAs AT ,k discussed here have the additional property that AT ,k ⊂ AT ,k+1. In the linear case AT ,k is a linear subspace of AT ,k+1 and AT ,k+1⊥ ⊂ AT ,k⊥, which allows e.g. the application of construction X to the NRT-codes AT ,k+1⊥ ⊂ AT ,k⊥.
Construction
The OOA AT ,k is obtained by taking the first bt+k runs of S (which gives an OOA(bt+k, s, Sb,∞, 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: 2024-09-05.
http://mint.sbg.ac.at/desc_OFromS.html