Computer experiments are constructed to simulate the behavior of complex physical systems. Uniform designs have good performance in computer experiments from several aspects. In practical use, the experimenter needs to choose a small size uniform design at the beginning of an experiment due to a limit of time, budget, resources, and so on, and later conduct a follow up experiment to obtain precious information about the system, that is, a sequential experiment. The Lee distance has been widely used in coding theory and its corresponding discrepancy is an important measure for constructing uniform designs. This paper proves that all the follow up designs of a uniform design are uniform and at least two of them can be used as optimal follow up experimental designs. Thus, it is not necessary that the union of any two uniform designs yields a uniform sequential design. Therefore, this article presents a theoretical justification for choosing the best follow up design of a uniform design to construct a uniform sequential design that involves a mixture of ω ≥ 1 factors with βk ≥ 2, 1 ≤ k ≤ ω levels. For illustration of the usage of the proposed results, a closer look is given at using these results for the most extensively used six particular cases, three symmetric and three asymmetric designs, which are often met in practice.