D-optimal fractions of three-level factorial designs with p factors are constructed for factorial effects models (2 < p < 4) and quadratic response surface models (2 < p < 5). These designs are generated using T. J. Mitchell's DETMAX algorithm and an algorithm which produces D-optimal balanced array designs. The design properties for the DETMAX designs and the balanced array designs are tabulated and compared with designs now in the literature. An example illustrating the application of these designs is given.
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