U*均匀设计的均匀性研究

On the Uniformity of U* Uniform Designs

  • 摘要: 本文以均匀设计在几何和物理意义下的均匀性等价准则为基础,研究了U*均匀设计的均匀性.利用本文结果,构造U*均匀设计使用表的运算量可减少为原来的s/2s-1(这里s为因素数),而且,当因素数为1/2φ(n+1)或1/2φ(n+1)-1时,不必进行任何均匀度评价也可直接给出其使用表,本文还从几何的角度说明了U*均匀设计最多只能安排1/2φ(n+1)个因素。

     

    Abstract: The uniformity of U* uniform designs is investigated based on the uniformity equivalence principle in the sense of physics and geometry. Using the results in this paper, we can construct the usable table of a U* uniform design in only s/2s-1 times of the calculation time being spent before (where s is the number of the factors). In addition, for the U* uniform designs with 1/2φ(n+1) or 1/2φ(n+1)-1 factors, the usable tables can be obtained immediately without any measurement for its uniformity. It is also shown from the viewpoint of geometry that no more than 1/2φ(n+1) factors can be arranged.

     

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