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.
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Acknowledgements
Both authors are partially supported by a INdAM GNAMPA 2017 project. RF acknowledges that the present research has been partially supported by MIUR grant Dipartimenti di Eccellenza 2018-2022 (E11G18000350001)
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Fontana, R., Rapallo, F. (2019). Unions of Orthogonal Arrays and Their Aberrations via Hilbert Bases. In: Petrucci, A., Racioppi, F., Verde, R. (eds) New Statistical Developments in Data Science. SIS 2017. Springer Proceedings in Mathematics & Statistics, vol 288. Springer, Cham. https://doi.org/10.1007/978-3-030-21158-5_31
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DOI: https://doi.org/10.1007/978-3-030-21158-5_31
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