Constructing optimal asymmetric combined designs via Lee discrepancy

The main objective of the present paper is to provide an answer to the question: How to construct optimal combined designs, whether regular or nonregular? In this paper, we take the Lee discrepancy as the optimality measure to construct the optimal mixed levels combined designs, which are most commonly used in practice. Equivalence between any combined design and its complementary combined design is investigated, which is a very useful constraint that reduce the search space for the optimal combined designs.