A class of mixed-level amplified designs and their space-filling properties

Abstract

With the increasing complexity of experimental scenarios, mixed-level designs with large size are urgently needed. A class of mixed-level designs are constructed through amplification, which enlarges both the run size and number of factors of initial design. The space-filling properties of amplified designs are discussed under generalized minimum aberration criterion, wordlength enumerator and maximin $L_2$-distance criterion, and attainable upper bound of maximin $L_2$-distance and lower bound of wordlength enumerator for amplified design are respectively obtained. Numerical examples demonstrate that the construction method of amplified designs is very simple and effective, and is recommended for application in high dimension topics of statistics or large-scale experiments.