A Scientific Tour on Orthogonal Arrays

Abstract

This paper gives a brief introduction to orthogonal arrays, including the definitions, basic questions, important theorems and applications. It establishes the connection between coding theory and orthogonal arrays. Based on coding theory, many construction methods of orthogonal arrays and linear programming bound, which is an improvement on Rao’s bound, are studied. Difference schemes and Hadamard matrices are also discussed in the paper, which contribute to the constructions of orthogonal arrays. Moreover, the paper brings in basic definitions and properties of mixed orthogonal arrays and focuses on problems and methods related to their constructions. As the main statistical application of orthogonal arrays, factorial experiments are then introduced, and ways orthogonal arrays can be used in this field is discussed. Further, the applications of orthogonal arrays in computer experiments and related structures are shown, including orthogonal Latin hypercube designs, nested orthogonal arrays, sliced orthogonal arrays, Latin squares and compound orthogonal arrays.