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. The best OAs according to the Generalized Minimum Aberration criterion can thereby be found simply by 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.

Unions of Orthogonal Arrays and Their Aberrations via Hilbert Bases / Fontana, Roberto; Rapallo, Fabio. - (2019), pp. 421-434. (Intervento presentato al convegno SIS 2017: New Statistical Developments in Data Science).

Unions of Orthogonal Arrays and Their Aberrations via Hilbert Bases

Fontana, Roberto;Rapallo, Fabio
2019

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. The best OAs according to the Generalized Minimum Aberration criterion can thereby be found simply by 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.
2019
978-3-030-21158-5
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Utilizza questo identificativo per citare o creare un link a questo documento: https://hdl.handle.net/11583/2751406
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