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Discrepancy measure can be utilized as a uniformity measure for comparing factorial designs. A so-called discrete discrepancy has been used to evaluate the uniformity of factorials. In this paper we give linkages among uniformity measured by the discrete discrepancy, generalized minimum aberration, minimum moment aberration and uniformity measured by the centered L2- discrepancy/the wrap-around L2-discrepancy. These close linkages provide a significant justification for the discrete discrepancy used to measure uniformity of factorial designs. © Springer-Verlag 2004.