Level permutation method for constructing uniform designs under the wrap-around L2-discrepancy

A new method for constructing uniform designs under the wrap-around L"2-discrepancy by permuting levels of factors is provided. By considering level permutation, the relationship between average wrap-around L"2-discrepancy and generalized wordlength pattern is obtained. Based on it, a general method for searching designs with smaller wrap-around L"2-discrepancies is proposed. Some special properties of wrap-around L"2-discrepancy can be used to make our algorithm much more efficient. Numerical results indicate that our method is better than existing ones.