Recently a computational-based experimental design strategy called rerandomization has been
proposed as an alternative or complement to traditional blocked designs. The idea of rerandomization is to
remove, from consideration, those allocations with large imbalances in observed covariates according to a
balance criterion, and then randomize within the set of acceptable allocations. Based on the Mahalanobis
distance criterion for balancing the covariates, we show that asymptotic inference to the population, from which
the units in the sample are randomly drawn, is possible using only the set of best, or ‘optimal’, allocations.
Finally, we show that for the optimal and near optimal designs, the quite complex asymptotic sampling
distribution derived by Li et al. (2018), is well approximated by a normal distribution.