The warp-around L<,2>-discrepancy has been commonly used in experimental designs. In this paper, some lower bounds of the warp-around L<,2>-discrepancy for asymmetrical U-type designs are given and the expectation and variance of midpoint Latin hypercube designs are also obtained. Relationships between midpoint Latin hypercube designs and uniform designs for symmetric and asymmetric cases are discussed in the sense of comparing the lower bound and the expectation of square warp-around L<,2>-discrepancy of U-type designs. Some comparisons between simple random sampling and the lower bounds of U-type designs are given.
展开▼
