Abstract
It is known (cf. Dodge (1985) and Kageyama (1985)) that the minimum number of experimental units for a block design with v treatments and b blocks to be connected is v+ b−1. This minimum number may not be attainable, however, when it is required that the design in question should satisfy certain additional conditions on treatment replications and/or block sizes or have certain additional properties, such as variance balance, efficiency balance and/or pairwise balance. In this paper, the problem of determining the minimum number of experimental units in connected block designs satisfying such additional requirements is considered. Some of the results derived are extensions of those given by Kageyama (1985), some other results are new.
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