On the Uniformity of U^* Uniform Designs

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 1/2φ(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.