Near-factorial experiments in nested row–column designs regulating efficiencies

We propose a method for constructing a nested row–column design d 0 , involving a control treatment and v test treatments, starting from a Youden or Latin square T and an incomplete block design d. It is shown how the choice of T and d regulates the efficiency factors of d 0 . Special attention is given to the case when the v test treatments have a factorial structure, and for appropriately chosen d, an admissibility property of d 0 , among all comparable designs, is established. Illustrative examples are given.