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Generate the needed Plackett-Burman design with the minimum number of runs, to study 8 factors and write down the design matrix for these eight factors.

Generate the needed Plackett-Burman design with the minimum number of runs, to study 8 factors and write down the design matrix for these eight factors. Can this design estimate all the main effects? Can this design estimate any 2-factor interactions? Justify all your answers.

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