Unions of Orthogonal Arrays and Their Aberrations via Hilbert Bases

Abstract

We generate all the Orthogonal Arrays (OAs) of a given size n and strength t as the union of a collection of OAs which belong to an inclusion-minimal set of OAs. We derive a formula for computing the (Generalized) Word Length Pattern of a union of OAs that makes use of their polynomial counting functions. In this way the best OAs according to the Generalized Minimum Aberration criterion can be found by simply exploring a relatively small set of counting functions. The classes of OAs with 5 binary factors, strength 2, and sizes 16 and 20 are fully described.

On the aberrations of mixed level orthogonal arrays with removed runs

“…Now we show some formulae to decompose the GWLP of a fraction. The proof of the first result can be found in [6]. The subsequent results exploit the results in Prop.…”