Before revision:  When the potential outcome is a linear function of a unit effect, a time effect, and observed discrete covariates, we provide an analytically feasible solution to the  design problem where the variance of the estimator for the treatment effect is at most 1+O(1/N^2) times the variance of the optimal design, where N is the number of units.
After revision:  When the potential outcome is a linear function of a unit effect, a time effect, and observed discrete covariates, we provide an analytically feasible solution to the design problem where the variance of the treatment effect estimator is at most 1+O(1/N^2) times the variance of the optimal design, where N is the number of units.