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A method that makes use of combinatorics for selecting N objects out of distinguishable objects is developed for constructing D-optimal N-point exact designs. The difficulties which are experienced in the variance exchange algorithms for constructing D-optimal exact designs, such as cycling, slow convergence and failure to converge to the desired optimum, are not experienced by this method. The method converges rapidly and absolutely to the desired N-point D-optimal design and is effective for determining optimal designs in block experiments as well as in non-block experiments for finite or infinite number of support points in the space of trials.

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