Abstract: We propose several infinite classes of new uniform designs under the discrete discrepancy criterion. The construction is based on combinatorial configurations, that is, partitionable t-designs; hence, it dose not require a computer search. Moreover, we explore certain complex structures within the proposed uniform designs. We find that some of the designs have nested or sliced subdesigns that are also uniform designs under the discrete discrepancy. The proposed uniform designs may find many applications in statistics, including computer experiments, sequential experiments, drug combination studies, and cross-validation.

Key words and phrases: Combinatorial construction, discrete discrepancy, nested and sliced design, uniformity.