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Biometrika 1986 73(2):289-299; doi:10.1093/biomet/73.2.289
© 1986 by Biometrika Trust
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Triangles and efficiency factors

LINDSAY J. PATERSON and PETER WILD

Department of Actuarial Mathematics and Statistics, Heriot- Watt University Edinburgh EH14 4AS, U.K.
Department of Mathematics, Royal Holloway College, University of London Egham, Surrey, TW2O 0EX, U.K.

We show that the number of triangles in the variety-concurrence graph of a regular-graph design can be used to derive upper bounds on the hatmonic-mean efficiency factor. The best alpha-lattice designs and the best cyclic designs have efficiency factors very close to the bounds. Our investigation gives insight into the structure of such designs. We see also that a certain type of regular-graph group-divisible design has a minimal number of triangles.

Key Words: Alpha-lattice design • Cyclic design • Incomplete block design • Upper bound on efficiency factor • Variety-concurrence graph


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