Triangles and efficiency factors

Lindsay J Paterson, Peter Wild

Research output: Contribution to journalArticle


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. © 1986 Biometrika Trust.

Original languageEnglish
Pages (from-to)289-299
Number of pages11
Issue number2
Publication statusPublished - Aug 1986


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

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    Paterson, L. J., & Wild, P. (1986). Triangles and efficiency factors. Biometrika, 73(2), 289-299.