A class of non binary unequally replicated E-optimal designs (Q1099552)

In a situation where the given set of parameters (b, k and v) precludes the existence of any known optimal block designs, but an optimal block design is known to exist with parameters b, k and \(v^*>v\), a new design is shown to be useful. This (b,k,v) design is obtained from the \((b,k,v^*)\) optimal design by collapsing the classes of a suitable partition of the treatment set (of the latter design) to treatments (of the former). We call the new design a quotient of the original design. Although the quotient is non binary and unequally replicated, it turns out to be E-optimal with the class of all proper and connected designs with b, k and v, provided the replication number of the optimal design we start with is not too large.