An effective approach for the optimum addition of runs to three-level uniform designs

Suppose that an experimenter begins the experimentation using three-level uniform designs. After the experiment is over or during the experimentation, some additional resources become available and the experimenter can afford more runs to the design. The full design obtained by augmenting the additional runs to those of the original design is called as extended design. The extended designs have been applied into computer experiments, microarray experiments and numerical integration. How does the experimenter pick the additional runs and augment the original design so as to get an optimal extended design? The main objective of the present paper is to provide an answer to this question.