Cyclic designs and factorial designs

Among R. C. Bose's many important contributions to the Design of Experiments are (i) the construction and assessment of confounded symmetrical factorial designs by using finite geometry, (ii) the construction of incomplete-block designs by generating all distinct translates of one or more subsets of an Abelian group (sometimes, but not necessarily, cyclic). Recent work extends theory (i) to all factorial designs and theory (ii) to generalized cyclic designs with many block systems, in a unified framework based on Abelian groups. In particular, the characters of Abelian groups can be used to determine the confounding patterns in the former and the efficiency factors in the latter.