A REVIEW OF BOUNDS FOR THE EFFICIENCY FACTOR OF BLOCK DESIGNS

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.