The relationship between admissible incomplete block designs for confidence intervals with maximal coverage probability for treatment-control contrasts and optimal designs for estimation is investigated. For certain types of designs, admissible designs are shown to be precisely those with the number of replications of the control less than or equal to that of an optimal design. Moreover, admissible designs are the Bayes optimal designs for a class of priors.
"On admissibility and optimality of treatment-control designs." Ann. Statist. 24 (5) 2097 - 2107, October 1996. https://doi.org/10.1214/aos/1069362312