  Rerandomization utilizes modern computing ability to search for covariate
balance improved experimental design while adhering to the randomization
principle originally advocated by RA Fisher. Conditionally affinely invariant
rerandomization has the ``Equal Percent Variance Reducing'' property on subsets
of conditionally ellipsoidally symmetric covariates. It is suitable to deal
with covariates of varying importance or mixed types and usually produces
multiple balance scores. ``Unified'' and `` intersection'' methods are common
ways of deciding on multiple scores. In general, `` intersection'' methods are
computationally more efficient but asymptotically inadmissible. As
computational cost is not a major concern in experimental design, we recommend
``unified'' methods to build admissible criteria for rerandomization
