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Some results on two-level regular designs with multi block variables containing clear effects. (English) Zbl 1432.62267

Summary: In this paper, the idea of clear effects is extended to the case of blocked regular \(2^{n-m}\) designs with multi block variables. Some necessary and sufficient conditions on the existence of clear treatment main effects and clear treatment two-factor interactions (2fi’s) in \(2^{n-m}:2^l\) designs with resolution III, IV\(^-\) and IV are obtained, where the notation \(2^{n-m}:2^l\) means that there are \(n\) treatment factors, \(m\) treatment defining words and \(l\) block variables. We discuss how to find \(2^{n-m}:2^l\) designs with the maximum number of clear 2fi’s with resolution III, IV\(^-\) or IV, and present some 16-, 32-, 64-run designs containing the maximum number of clear 2fi’s in tables.

MSC:

62K15 Factorial statistical designs
62K05 Optimal statistical designs
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