Abstract
In a situation where the given set of parameters (b, k andv) precludes the existence of any known optimal block designs, but an optimal block design is known to exist with parametersb, k andv*>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 paritition 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 beE-optimal within the class of all proper and connected designs withb, k andv, provided the replication number of the optimal design we start with is not too large.
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Bagchi, S. A class of non binary unequally replicatedE-optimal designs. Metrika 35, 1–12 (1988). https://doi.org/10.1007/BF02613280
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DOI: https://doi.org/10.1007/BF02613280