D-optimal block designs with at most six varieties |
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Authors: | N. Gaffke |
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Affiliation: | Rheinisch Westfalische Vechnische Hochschule Aachen, Institut für Statistik und Wirtschaftsmathematik, D-5100 Avchen, West Germany |
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Abstract: | For given positive integers v, b, and k (all of them ≥2) a block design is a k × b array of the variety labels 1,…,v with blocks as columns. For the usual one-way heterogeneity model in standard form the problem is studied of finding a D-optimal block design for estimating the variety contrasts, when no balanced block design (BBD) exists. The paper presents solutions to this problem for v≤6. The results on D-optimality are derived from a graph-theoretic context. Block designs can be considered as multigraphs, and a block design is D-optimal iff its multigraph has greatest complexity (=number of spanning trees). |
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Keywords: | Primary 62K05, 62K10 Secondary 05C05, 05C35 Optimality Criterion Multigraph Spanning Tree Balanced Block Design Regular Graph Design |
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