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A general method for obtaining highly efficient factorial designs ofrelatively small sizes is developed for cDNA microarray experiments. The methodallows the main effects and interactions of successive orders to be of possiblyunequal importance. First, the approximate theory is em-ployed to get anoptimal design measure which is then discretized. It is, however, observed thata na\"ive discretization may fail to yield an exact design of the stipulatedsize and, even when it yields such an exact design, there is often scope forimprovement in efficiency. To address these issues, we propose a step-up/downprocedure which is seen to work very well. The resulting highly efficientdesigns are found to remain almost free from possible dye-color effects under asuitable dye-color assignment. They are also seen to be quite robust toheteroscedasticity as may be caused by biological variability. We focus on thebaseline and all-to-next parametrizations but our method works equally wellalso for hybrids of the two and other parametrizations.

Highly Efficient Factorial Designs for cDNA Microarray Experiments: Use of Approximate Theory Together with a Step-up Step-down Procedure