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n-detection test sets for stuck-at faults have been shown to be useful in detecting unmodeled defects. It was also shown that a set of faults, called maximally dominating faults, can play an important role in controlling the increase in the size of an n-detection test set as n is increased. In an earlier work, a superset of the maximally dominating fault set was used. In this work, we propose a method to determine exact sets of maximally dominating faults. We also define a new type of n-detection test sets based on the exact set of maximally dominating faults. We present experimental results to demonstrate the usefulness of this exact set in producing high-quality n-detection test sets.