A search of maximum generalized resolution quaternary-code designs via integer linear programming
| Autor: | Tai-Chi Wang, Frederick Kin Hing Phoa, Shu-Ching Lin |
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| Rok vydání: | 2014 |
| Předmět: |
Statistics and Probability
Discrete mathematics Class (set theory) Design of experiments 010401 analytical chemistry Fractional factorial design 01 natural sciences 0104 chemical sciences Theoretical Computer Science 010104 statistics & probability Computational Theory and Mathematics Code (cryptography) 0101 mathematics Statistics Probability and Uncertainty Aliasing (computing) Integer programming Mathematics Resolution (algebra) |
| Zdroj: | Statistics and Computing. 26:277-283 |
| ISSN: | 1573-1375 0960-3174 |
| DOI: | 10.1007/s11222-014-9496-7 |
| Popis: | Quaternary-code (QC) designs, an attractive class of nonregular fractional factorial designs, have received much attention due to their theoretical elegance and practical applicability. Some recent works of QC designs revealed their good properties over their regular counterparts under commonly used criteria. We develop an optimization tool that can maximize the generalized resolution of a QC design of a given size. The problem can be recast as an integer linear programming (ILP) problem through a linear simplification that combines the $$k$$k- and $$a$$a-equations, even though the generalized resolution does not linearly depend on the aliasing indexes. The ILP surprisingly improves a class of $$(1/16)$$(1/16)th-fraction QC designs with higher generalized resolutions. It also applies to obtain some $$(1/64)$$(1/64)th-fraction QC designs with maximum generalized resolutions, and these QC designs generally have higher generalized resolutions than the regular designs of the same size. |
| Databáze: | OpenAIRE |
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