Incomplete Block Designs for Comparing Treatments with a Control (V): Optimal Designs for p = 6, k = 3.

The present paper continues the study of balanced treatment incomplete block BTIB designs initiated previously. This class of designs was proposed for the problem of comparing simultaneously p or 2 test treatments with a control treatment when the observations are taken in blocks of common size k p1. The conjectured minimal complete class of generator designs, a catalog of admissible designs, and tables of optimal designs are given for p 6, k 3. The efficiency of the optimal BTIB design relative to that of replications of a BIB design is computed for situations in which both provide the same probability guarantee for the multiple comparisons with a control problem.