Constant block sum PBIB designs based on tetrahedral and cubical association schemes

In biomedical studies, particularly those involving animals, the carryover effects from previous experiments necessitate a repeated measures approach. In this context, constant block-sum designs are particularly relevant, especially in situations where treatments are quantitative and there's a desire for all units to be exposed to the same cumulative dose at the experiment's conclusion.

This article discusses two distinct methods for constructing constant block-sum PBIB designs, supplemented with illustrative examples.

The most advantage of these designs is that if we wish to do experiment in subsequence form, the set of experimental units used, as homogeneous and thus can reuse them in later subsequent experiments.