The problem of finding optimal incomplete blocks designs for comparing $p$ test treatments with a control is studied. B.I.B. designs are found to be $D$-optimal. $A$- and $E$-optimal designs are also obtained. For a large class of functions $\phi$, conditions for a design to be $\phi$-optimal are found. Most of the optimal designs are certain types of B.T.I.B. designs, introduced by Bechhofer and Tamhane (1981), which are binary in test treatments.
"Optimal Incomplete Block Designs for Comparing Treatments with a Control." Ann. Statist. 11 (1) 258 - 266, March, 1983. https://doi.org/10.1214/aos/1176346076