Generalized Rao Bound for OOAs

Martin and Stinson [1, Theorem 3.5] show that for an even k ≥ 2 an ordered orthogonal array OOA(M, s, Sb, T , k) can only exist if

MVb(s,T )(k/2),

where Vb(s,T )(r) denotes the volume of a ball with radius r in the NRT-space Sb(s,T ).

The dual to the Rao bound for OOAs is the Hamming bound or sphere-packing bound in NRT space, which was established in [2, Theorem 3]. Using duality [3], it yields the Rao bound for linear OOAs.

It is shown in [4, Section 5] that the generalized Rao bound follows also from the linear programming bound for OOAs.

See also

References

[1]William J. Martin and Douglas R. Stinson.
A generalized Rao bound for ordered orthogonal arrays and (t, m, s)-nets.
Canadian Mathematical Bulletin, 42(3):359–370, 1999.
MR1703696 (2000e:05030)
[2]Michael Yu. Rosenbloom and Michael A. Tsfasman.
Codes for the m-metric.
Problems of Information Transmission, 33:55–63, 1997.
[3]Harald Niederreiter and Gottlieb Pirsic.
Duality for digital nets and its applications.
Acta Arithmetica, 97(2):173–182, 2001.
MR1824983 (2001m:11130)
[4]Jürgen Bierbrauer.
A direct approach to linear programming bounds for codes and tms-nets.
Designs, Codes and Cryptography, 42(2):127–143, February 2007.
doi:10.1007/s10623-006-9025-6 MR2287187

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. “Generalized Rao Bound for OOAs.” From MinT—the database of optimal net, code, OA, and OOA parameters. Version: 2008-04-04. http://mint.sbg.ac.at/desc_OBoundRao.html

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