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Fractional Factorial Plans

TLDR
Fractional plans and orthogonal arrays have been extensively studied in the literature, see as discussed by the authors for a survey of some of the most relevant works. But nonexistence of fractional plans has been discussed.
Abstract
Fractional Plans and Orthogonal Arrays. Symmetric Orthogonal Arrays. Asymmetric Orthogonal Arrays. Some Results on Nonexistence. More on Optimal Fractional Plans and Related Topics. Trend-Free Plans and Blocking. Some Further Developments. Appendix. References. Index.

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Optimum Design for Estimation of Regression Parameters in Multi-Factor Set-Up

TL;DR: In this paper, the authors extended these results and proposed an extended mixed orthogonal array (EMOA) for the multi-factor set-up where the factorial effects involving at most t (≤m) factors are orthogonally estimable.
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Split-plot designs for multistage experimentation

TL;DR: In this article, the authors present a methodology for constructing two-level split-plot and multistage experiments based on the Kronecker product representation of orthogonal designs and can be used for any number of stages.
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Some results on generalized minimum aberration for symmetrical fractional factorial designs

TL;DR: In this article, the generalized minimum aberration coincides with the nearest balance criterion for symmetrical factorials, which is a generalization of the related results in Tang (2001).
References
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Non-Orthogonal Designs of Even Resolution*

TL;DR: In this paper, it was shown that the smallest resolution 4 designs for n factors at two levels must contain at least 2n runs, and that "foldover" designs are available with 2 n runs.