Abstract:

Space-filling designs are widely used in computer experiments due to their favorable properties, and the construction of large-scale space-filling designs is becoming increasingly important with the realistic demand for an increasing number of runs and factors in experimental scenarios. In this paper, two methods are proposed to construct four-level space-filling designs from two-level designs based on rotation methods, and the connections between the constructed four-level space-filling designs and initial two-level designs are investigated under the wordlength enumerator and stratification pattern enumerator, respectively. The connection between their wordlength enumerator and stratification pattern enumerator and the distance distribution of initial two-level designs is established. Analytical relationships between the generalized wordlength pattern and space-filling pattern of the constructed four-level space-filling design and the ones of its initial two-level design are given. The lower bounds of wordlength enumerator and stratification pattern enumerator of the constructed four-level space-filling design are obtained. Numerical examples show that the constructed four-level space-filling designs in this paper have good space-filling and stratification properties, the construction methods are simple and can be applied to large scale experimental scenarios and generalized to the construction of multi-level and mixed-level space-filling designs.

Key words: space-filling designs, rotation method, wordlength enumerator, stratification pattern enumerator