OAs with Strength 3, b ≠ 2, and m > 3 Are Always Embeddable
In [1, Theorem 3] and [2, Theorem 4] it is shown that linear orthogonal arrays OA(bm, s,Fb, 3) with b ≠ 2 and either b odd or m > 3 are always embeddable in an ordered orthogonal array OOA with depth T > 1.
References
| [1] | Wolfgang Ch. Schmid. (t, m, s)-Nets: Digital Construction and Combinatorial Aspects. PhD thesis, University of Salzburg, Austria, 1995. |
| [2] | Kenneth Mark Lawrence, Arijit Mahalanabis, Gary L. Mullen, and Wolfgang Ch. Schmid. Construction of digital (t, m, s)-nets from linear codes. In S. D. Cohen and Harald Niederreiter, editors, Finite Fields and Applications, volume 233 of Lect. Note Series of the London Math. Soc., pages 189–208. Cambridge University Press, 1996. |
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. “OAs with Strength 3, b ≠ 2, and m > 3 Are Always Embeddable.”
From MinT—the database of optimal net, code, OA, and OOA parameters.
Version: 2015-09-03.
http://mint.sbg.ac.at/desc_OK3Embeddable.html