Balanced Incomplete Block Designs

Block designs are useful in experimental design when the experimental material is not uniform but can be divided into homogeneous blocks. Typically, blocks cannot contain all the treatments, so incomplete block designs are used. The condition of balance, if it can be achieved, guarantees that the designs are optimal in minimizing the variance of treatment differences.

This entry provides a survey of balanced incomplete block designs (BIBDs). It discusses necessary conditions on the parameters for the existence of the designs and optimality results. It also provides a brief introduction to constructions of BIBDs using difference families, finite fields, or recursive methods, and some generalizations, including pointers about what to do if no BIBD is available.