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Families of proper generalized neighbor designs. (English) Zbl 1110.62096
Summary: A generalized neighbor design relaxes the equality condition on the number of times two treatments occur as neighbors in the design. In this article we have constructed a new series of generalized neighbor designs with equal block sizes, a series of neighbor designs of D. H. Rees [Some designs of use in serology. Biometrics 23, 779–791 (1967)] and a series of neighbor designs with two distinct block sizes. Two more new series of \(GN_{2}\) designs are also constructed for even number of treatments. It has been shown that quasi neighbor designs introduced by D. A. Preece [Balanced Ouchterlony neighbour designs and quasi-Rees neighbour designs. J. Comb. Math. Comb. Comput. 15, 197–219 (1994; Zbl 0806.05022)] are special cases of generalized neighbor designs with \(t=2\). All the designs given here are binary. A new definition – partially balanced circuit design – is introduced which is a special case of generalized neighbor designs with binary blocks.

MSC:
62K10 Statistical block designs
05B05 Combinatorial aspects of block designs
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