Construction of mixed orthogonal arrays with high strength
针对强度t≥3的混合正交数组存在性知识有限的问题，提出了利用低强度正交划分和正交数组构造对称与非对称高强度正交数组的新方法，解决了Hedayat等人1999年提出的开放问题，构造的数组灵活且实用。
A considerable portion of the work on mixed orthogonal arrays applies specifically to arrays of strength 2. Although strength t=2 is arguably the most important case for statistical applications, there is an urgent need for better methods for t≥3. However, the knowledge on the existence of arrays for t≥3 is rather limited. In this paper, new construction methods for symmetric and asymmetric orthogonal arrays (OAs) with high strength are proposed by using lower strength orthogonal partitions of spaces and OAs. A positive answer is provided to the open problem in Hedayat, Sloane and Stufken (Orthogonal Arrays: Theory and Applications (1999) Springer) on developing better methods and tools for the construction of mixed orthogonal arrays with strength t≥3. Not only are the methods straightforward, but also they are useful for constructing symmetric or asymmetric OAs of arbitrary strengths, numbers of levels and various sizes. The constructed OAs can be utilized to generate more OAs. The resulting OAs have a high degree of flexibility and many other desirable properties. Some selective OAs are tabulated for practical uses.