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.

翻译：方形阵列中的增强设计可以从较小的行列设计（即收缩设计）推导得出。这种收缩设计先前也曾用于生成两重复可解不完全区组设计。我们通过建立增强设计的平均效率因子与其收缩设计平均效率因子之间的联系，证明了收缩设计在这两种用途上的平行性，从而证实了最近提出的一个猜想。