Construction of four-level and mixed-level designs with zero Lee discrepancy (Q2303035)

From the authors' abstract: ``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.'' The construction of the relevant fractional factorial designs is based on standard arguments, such as a replacement rule defined through the Gray map. Such a rule is used to define four-level factors from pairs of two-level factors.