Summary
A connection between a balanced fractional 2m factorial design of resolutionV and a balanced array of strength 4 with index set {μ 0,μ 0,μ 1,μ 2,μ 3,μ 4} has been established by Srivastava [3]. The purpose of this paper is to generalize his results by investigating the combinatorial property of a fractionT and the algebraic structure of the information matrix of the fractional design. Main results are: A necessary and sufficient condition for a fractional 2m factorial designT of resolution 2l+1 to be balanced is thatT is a balanced array of strength 2l with index set {μ 0,μ 1,μ 2, ⋯,μ 21} provided the information matrixM is nonsingular.
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References
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Yamamoto, S., Shirakura, T. & Kuwada, M. Balanced arrays of strength 2l and balanced fractional 2m factorial designs. Ann Inst Stat Math 27, 143–157 (1975). https://doi.org/10.1007/BF02504632
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DOI: https://doi.org/10.1007/BF02504632