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/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.