A-optimal block designs for comparing test treatments with a control (Q1094056)

We consider the problem of comparing test treatments with a control in a proper block design. We give conditions on the parameters of both R-type and S-type designs that guarantee their A-optimality, and demonstrate how these conditions can be used to obtain families of A-optimal designs. We give an example for the construction of the desired S-type designs. A table with optimal R-type designs (3\(\leq k\leq 10\), \(k\leq v\leq 30)\) is also given.