The Application Of Lattice Points Method On Uniform Designs In An Arbitrary Convex Polyhedron

As an important method of fractional factorial design,uniform design has been general-ized and used widely.Lattice design is a vital principle of uniform design,and Lattice points method is also a classical method for constructing uniform design.But in the last papers,this method is only limited in the construction in unit cube,and not mentioned for constructing uniform designs in an arbitrary convex polyhedron which is more far-ranging applied in the actual production(Like the mixture uniform design).For constructing uniform design in an convex polyhedron,tranformation is the usural method.This paper improved the traditional lattice points method,and give two new ways of distributing points in an arbitrary convex polyhedron.At the same time we also modify the potential function,use it as a kind of new measure of uniformity.Add the arithmetic of random optimize and obtain a new method of constructing uniform design in an arbitrary convex polyhedron.