Revisiting Randomization with the Cube Method

We introduce a new randomization procedure for experiments based on the cube method, which achieves near-exact covariate balance. This ensures compliance with standard balance tests and allows for balancing on many covariates, enabling more precise estimation of treatment effects using pre-experimental information. We derive theoretical bounds on imbalance as functions of sample size and covariate dimension, and establish consistency and asymptotic normality of the resulting estimators. Simulations show substantial improvements in precision and covariate balance over existing methods, particularly when the number of covariates is large.