A survey of nested designs

A nest with parameters (r,k,λ)→(r′,k′,λ′) is a BIBD on (b,v,r,k,λ) where each block has a distinguished sublock of cardinality k, the sublocks forming a (b,v,r,k,λ)-design.These designs are ‘nested’ in the sense of W.T. Federer (1972), who recommended the use of these designs for the sequential addition of periods in marketing experiments in order to retain Youden design properties as rows are added. Note that for a Youden design, the b columns and v treatments are in an SBIBD arrangement with parameters v=b, k=r, and λ.