摘要
Orthogonal arrays (OAs), mixed level or fixed level (asymmetric or symmetric), 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 establish a general "expansive replacement method" for constructing mixedlevel OAs of an arbitrary strength. As a consequence, a positive answer to the question about orthogonal arrays posed by Hedayat, Sloane and Stufken is given. Some series of mixed level OAs of strength ≥3 are produced.
Orthogonal arrays （OAs）, mixed level or fixed level （asymmetric or symmetric）, 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 establish a general ＂expansive replacement method＂ for constructing mixed- level OAs of an arbitrary strength. As a consequence, a positive answer to the question about orthogonal arrays posed by Hedayat, Sloane and Stufken is given. Some series of mixed level OAs of strength ≥ 3 are produced.
基金
supported by National Natural Science Foundation of China (Grant Nos.11271280 and 10831002)
