The purpose of this paper is to find and construct optimal designs for estimating the standardized linear and quadratic contrasts in fractional factorials withkfactors, each at 3 levels, when the number of runs or assemblies isN. The caseN=3mis examined, the notion of Balanced Arraysorfor short, is introduced and the optimalis specified. It is shown that forN=9mthe orthogonal arrayorfor short, is theφ-optimal design. IfN=9m+3 andN=9m+6 the optimal designs arewhich are specified for every value ofNandk. In the caseN=9m+3 andk=3 the optimalare constructed by augmentingby three rows which are specified. If thedoes not exist, algorithms are developed to construct the optimal. ForN=9m+6 andk=3 the optimalare constructed by augmentingby six rows, which are specified, otherwise algorithms are developed. Under optimal, the estimators of linear and quadratic contrasts are uncorrelated. The casesN=12,15,21,24,30,33 are examined in detail and optimalare presented for different values of the numberkof factors. [ABSTRACT FROM AUTHOR]
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