A Review of Bounds for the Efficiency Factor of Block Designs

summary This paper draws together bounds for the efficiency factor of block designs, starting with the papers of Conniffe & Stone (1974) and Williams & Patterson (1977). By extending the methods of Jarrett (1983), firstly to cover supercomplete block designs and then to cover resolvable designs, a set of bounds is obtained which provides the best current bounds for any block design with equal replication and equal block size, including resolvable designs and two‐replicate resolvable designs as special cases. The bounds given for non‐resolvable designs apply strictly only to designs which are either regular‐graph (John & Mitchell, 1977) or whose duals are regular‐graph. It is conjectured (John & Williams, 1982) that they are in fact global bounds. Similar qualifications apply to the bounds for resolvable designs.