Construction of four-level and mixed-level designs with zero Lee discrepancy

The uniformity criterion under Lee discrepancy favors designs with the smallest Lee discrepancy value. Based on quaternary codes, the present paper explores the construction of four-level and mixed two- and four-level fractional factorial designs with zero Lee discrepancy. A general construction method is provided, and our theoretic results show that designs with zero Lee discrepancy can be obtained from two-level full factorial designs. When measuring uniformity by Lee discrepancy, designs with a value of zero apparently are optimal. In particular, an additional lower bound on Lee discrepancy is not required.