The Existence of Mixed Orthogonal Arrays with Four and Five Factors of Strength Two


  • Contract grant sponsor: Natural Science Foundation of China; Contract grant numbers: 61071221; 11271004 (J. L.); 11222113 (L. J.); Contract grant sponsor: Youth Science Foundation of China; Contract grant number: 11201114 (G. C.).


Symmetric orthogonal arrays and mixed orthogonal arrays are useful in the design of various experiments. They are also a fundamental tool in the construction of various combinatorial configurations. In this paper, we investigated the mixed orthogonal arrays with four and five factors of strength two, and proved that the necessary conditions of such mixed orthogonal arrays are also sufficient with several exceptions and one possible exception.