Abstract
In this paper, we investigate a new analytical expression of the centered L2-discrepancy measure of uniformity for mixed two and three-level U-type designs in depth. Based on this new formulation, we present a new lower bound to the centered L2-discrepancy for U-type designs with mixed two and three-level, which can be used as a benchmark in searching uniform U-type designs. We also describe a necessary condition for the existence of uniform designs meeting this lower bound. For illustration of the usage of our theoretical results, a catalog of lower bounds for U-type designs in U(n;2m1×3m2) is tabulated, where 0≤m1≤10, 0≤m2<25 and 6≤n<60.
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