A note on the construction of augmented designs in square arrays

An augmented design in a square array can be derived from a smaller row-column design (the contraction). Such a contraction has also previously been used to generate a two-replicate resolvable incomplete block design. We demonstrate a parallel between these two uses of the contraction and thereby establish a recently proposed conjecture by linking the average efficiency factor of the augmented design with that of its contraction.
Comment: 7 pages