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