Construction of $2^m4^n$ Designs via a Grouping Scheme
Open Access
- 1 December 1989
- journal article
- Published by Institute of Mathematical Statistics in The Annals of Statistics
- Vol. 17 (4) , 1880-1885
- https://doi.org/10.1214/aos/1176347399
Abstract
We develop a method for grouping the $2^k - 1$ factorial effects in a 2-level factorial design into mutually exclusive sets of the form $(s, t, st)$, where $st$ is the generalized interaction of effects $s$ and $t$. As an application, we construct orthogonal arrays $OA(2^k, 2^m4^n, 2)$ of size $2^k, m$ constraints with 2 levels and $n$ constraints with 4 levels in the construction cannot be further improved. In this sense our grouping scheme is optimal. We discuss the advantages of the present approach over other construction methods.
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