| Maximin distance designs as an important class of space-filling designs are widely used today, yet their constructions are challenging. In this article, we develop a 3-step procedure which can efficiently generate maximin distance Latin hypercube designs and maximin distance fractional factorial designs. This new method selects existing efficient low-level designs to generate high-level maximin distance designs via level expansion. The generated maximin distance designs are of flexible run and factor sizes and also have robust pairwise correlations. To justify this method, we derive the relationships of the distance distributions between the initial low-level designs and the generated high-level designs. We also prove the relationships between the generalized word length patterns of the initial low-level designs and the distance distributions of the generated high-level designs. Examples are presented to show that this new method outperforms many current prevailing methods in generating maximin distance designs. |
