Uniformity of incomplete block designs

Incomplete block designs are a type of experimental design layout that has had widespread use in science and engineering. A balanced incomplete block design (BIB) can be characterised by the balanced arrangement of its design points. In this article, incomplete block designs will be investigated from a new perspective: the perspective of uniformity in distribution of design points. A design is of high uniformity, or low discrepancy, if its design points distribute uniformly over the entire design space. The authors use a general discrepancy measure to prove theoretically that BIBs are the most uniform ones among all binary incomplete block designs.