Grouped Orthogonal Arrays from Orthogonal Arrays and Difference Schemes

2026-07-02

AI Summary

This study addresses the design of efficient experiments for scenarios involving grouped factors—such as in computer experiments with structured inputs or physical experiments where inter-group factor interactions are negligible. By integrating orthogonal arrays with difference set constructions, the work introduces several novel combinatorial methods that substantially expand the design space of grouped orthogonal arrays. The resulting constructions yield a rich collection of new arrays that accommodate a greater number of groups and larger group sizes than previously available, thereby enriching existing catalogs. These advances significantly enhance the flexibility and efficiency of experimental designs in complex grouped-factor settings.

Abstract

Grouped orthogonal arrays were introduced to address experimental design problems arising in computer experiments with grouped inputs, as well as in physical experiments where interactions between factors from different groups are assumed to be negligible. Motivated by the growing need for flexible and efficient designs under such settings, this article develops several constructions to expand the existing catalogs of grouped orthogonal arrays. The proposed constructions provide a large collection of new grouped orthogonal arrays with significantly larger numbers of groups and group sizes.

Problem

• grouped orthogonal arrays
• experimental design
• computer experiments
• factor interactions
• difference schemes

Innovation

• Grouped Orthogonal Arrays
• Orthogonal Arrays
• Difference Schemes
• Experimental Design
• Factorial Experiments