MinT - Bound Derived from the LP Bound by Trinker

Bound Derived from the LP Bound by Trinker

In [1] Trinker shows that every ordered orthogonal array OOA(M, s, S_b, T , k) with

T ≥ 2,
k = sT – ⌈s(1/b + … +1/b^T)⌉, and
3 + k – 4b – 2kb – 2s + Ts(2b – 1) < 0

must satisfy the condition

N = b^Ts/M ≤ b $\displaystyle \left(\vphantom{1+\frac{(b−1)(k-sT−2(s−1)+\alpha}{2+k−4b−2kb−2s+Ts(2b−1)+\alpha}}\right.$ 1 + $\displaystyle {\frac{{(b−1)(k-sT−2(s−1)+\alpha}}{{2+k−4b−2kb−2s+Ts(2b−1)+\alpha}}}$ $\displaystyle \left.\vphantom{1+\frac{(b−1)(k-sT−2(s−1)+\alpha}{2+k−4b−2kb−2s+Ts(2b−1)+\alpha}}\right)$

with α = Ts – k mod 2.

The result is established by constructing an explicit solution to the linear programming bound for OOAs based on only three different types.

The region of parameters where this bound can be used is rather small (since k is determined by b, T , and s and the third condition must be met) and completely in inside the region where the (dual) Plotkin bound for OOAs is applicable. However, it often provides stronger results than the Plotkin bound.

References

[1]	Horst Trinker. Some improvements of the generalized Plotkin bound, September 2007. Preprint.

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. “Bound Derived from the LP Bound by Trinker.” From MinT—the database of optimal net, code, OA, and OOA parameters. Version: 2015-09-03. http://mint.sbg.ac.at/desc_OBoundTrinker.html

Show usage of this method