U~*均匀设计的均匀性研究

On the Uniformity of U~* Uniform Designs

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／２^（ｓ－１）（这里ｓ为因素数）．而且，当因素数为１／２ （ｎ＋１）或１／２ （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１／２ （ｎ＋１）个因素.

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/2^(s-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 1/2 (n+1) or 1/2 (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 1/2 (n+1) factors can be arranged.