Bayes $A$-optimal designs for the one-way and the two-way elimination of heterogeneity models and optimal $\Gamma$-minimax designs for the one-way elimination of heterogeneity model for experiments to compare test treatments with a control are given. Properties such as robustness, of these designs are studied. Optimality results are derived in the exact theory setup.
"Optimal Designs for Comparing Test Treatments with a Control Utilizing Prior Information." Ann. Statist. 20 (1) 216 - 237, March, 1992. https://doi.org/10.1214/aos/1176348519