| The uniform design is a very important type of design in experimental design.It is widely used in chemical experiments,industrial production,pharmaceutical research and other fields in view of its ability to reduce experimental costs at the actual projects.In a lot of practical cases.different facto rs may take different numbers of values.so the mixed-level uniform design is valued by many experiment arrangers.Since it is not reasonable to use the uniformity measure with the same weight for factors with different levels.the weighted discrete discrepancy was proposed in the existing literature.This paper discusses the construction method of mixed-level uniform designs under the weighted discrete discrepancy.The underlying method is to utilize some properties of partitioned difference families(PDFs)to obtain an infinite class of uniformly resolvable weighted balanced designs(URWBDs).which can directly produce corresponding uniform designs.We firstly give the steps of constructing a special class of PDFs.Then based on the connection between the construction method and finite field,we discuss the selection of blocks for PDFs.Subsequently,By using the finite field as a mathematical tool,we consider the difference of elements within or between the blocks of the PDFs and provide some properties.Moreover,we propose a new method for constructing the URWBDs and prove the existence of the URWBDs by applying these properties.Finally,according to the URWBDs.we obtain an infinite class of uniform designs under the weighted discrete discrepancy.In addition,some examples are presented to illustrate the methods. |
