Augmented block designs for unreplicated test treatments are investigated under the A- and MV-criteria with respect to control versus control, test versus test and control versus test comparisons. We derive design-independent lower bounds on these criteria over a wide class of competing designs. These bounds are useful benchmarks and the resulting expressions for efficiencies enable objective assessment of any given design under the A- and MV-criteria. It is seen that the use of BIB or PBIB designs or duals thereof often leads to very high efficiencies, which compare extremely well with algorithmic constructions. Our findings also cover the case of partial replication of some test treatments. Illustrative examples, including large-scale ones, are presented.

翻译：针对非重复试验处理的增广区组设计，在A-准则和MV-准则下，分别考察了对照处理间、试验处理间以及对照处理与试验处理间的比较。我们在一个广泛的竞争设计类别中，推导了这些准则下与设计无关的下界。这些下界可作为有效的基准，且由此得到的效率表达式能够客观评估任意给定设计在A-准则和MV-准则下的表现。研究表明，采用BIB或PBIB设计及其对偶设计往往能获得极高的效率，其效果与算法构造结果相当。本研究结论还涵盖了部分试验处理存在重复的情况，并给出了包括大规模场景在内的说明性示例。