标准混合差集矩阵的构造

ON THE CONSTRUCTION OF NORMAL MIXED DIFFERENCE MATRICES

通过利用差集矩阵和投影矩阵的正交分解之间的关系,首先提出了构造小的标准混合差集矩阵的一般方法.其次,给定一个阶为r+1的标准混合差集矩阵和一个阶为r的差集矩阵,首先提出了构造阶为r(r+1)的标准混合差集矩阵的一般方法.如果阶为r的差集矩阵不存在但一个试验次数为r^2的正交表存在,也可以通过它们构造阶数较大的标准混合差集矩阵.

By exploring the relationship between difference matrices and orthogonal decomposition of projection matrices, this paper presents a general method for constructing smaller normal mixed difference matrices. Moreover, given a normal mixed difference matrix of order r ＋ 1 and a difference matrix of order r, this paper also presents a general method for constructing a lager normal mixed difference matrix of order r（r ＋ 1）. Furthermore, if the difference matrix of order r does not exist but an orthogonal array of runs r2 exists, we can also construct a lager normal mixed difference matrix from the normal mixed difference matrix of order r ＋ 1 and the orthogonal array of runs r2.