Abstract
Discrepancy is a kind of important measure used in experimental designs. Among various existing discrepancies, the discrete discrepancy, centered L 2-(CD 2) and wrap-around L 2-discrepancy (WD 2) have been well justified and widely used. In this paper, using the second-order polynomials of indicator functions for these three discrepancies, we investigate the close relationships between them and the generalized wordlength pattern, and provide some conditions under which a design having one of these minimum discrepancies is equivalent to having generalized minimum aberration (GMA). These results provide further justifications for the criterion of GMA in terms of uniformity. In addition, the expressions of the discrepancies in the quadratic forms of the indicator functions are useful for us to find optimal designs under any of them.
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