Abstract
Zhang et al. (Stat Sinica 18:1689–1705, 2008) introduced an aliased effect-number pattern for two-level regular designs and proposed a general minimum lower-order confounding (GMC) criterion for choosing optimal designs. All the GMC \(2^{n-m}\) designs with \(N/4+1\le n\le N-1\) were constructed by Li et al. (Stat Sinica 21:1571–1589, 2011), Zhang and Cheng (J Stat Plan Inference 140:1719–1730, 2010) and Cheng and Zhang (J Stat Plan Inference 140:2384–2394, 2010), where \(N=2^{n-m}\) is run number and \(n\) is factor number. In this paper, we first study some further properties of GMC design, then we construct all the GMC \(2^{n-m}\) designs respectively with the three parameter cases of \(n\le N-1\): (i) \(m\le 4\), (ii) \(m\ge 5\) and \(n=(2^m-1)u+r\) for \(u>0\) and \(r=0,1,2\), and (iii) \(m\ge 5\) and \(n=(2^m-1)u+r\) for \(u\ge 0\) and \(r=2^m-3,2^m-2\).
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Acknowledgments
We would like to thank the Editor and the anonymous referee for their comments and suggestions which are very valuable in improving the paper. This work was supported by the NNSF of China grant Nos. 11171165, 11101074 and 10871104.
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Guo, B., Zhou, Q. & Zhang, R. Some results on constructing general minimum lower order confounding \(2^{n-m}\) designs for \(n\le 2^{n-m-2}\) . Metrika 77, 721–732 (2014). https://doi.org/10.1007/s00184-013-0461-9
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DOI: https://doi.org/10.1007/s00184-013-0461-9