Constructions of array type block designs and their statistical optimality and efficiency

在这项研究中，我们调查组合结构和统计最优性，效率的阵列类型区组设计，如分裂区组设计，BIB设计嵌套行和列，或网格设计。在规划这种设计时，重要的是要考虑最优性和效率。我们表明，如果使用平衡不完全裂区设计，则估计交互作用效应是最佳的。并且我们给出了这种设计的一些构造。此外，我们还得到了一个设计的效率因子可以显式得到的组合特征。另一方面，我们证明了网格区组设计可以作为一种有效的组检验方法应用于DNA文库筛选。并得到了网格设计的一些构造。

In this research, we investigate combinatorial constructions and statistical optimality, efficiency of array type block designs such as a split-block design, BIB design with nested rows and columns, or grid designs. In planning such design, it is important to consider the optimality and efficiency. We showed that if a balanced incomplete split-block design is utilized, it is optimal to estimate the interaction effects. And we gave some constructions of such designs. Moreover, we obtain combinatorial characterization that the efficiency factor of a design can be obtained explicitly.On the other hand, we showed that a grid block design can be applied to a DNA library screening as an efficient way of group testing. And some constructions of a grid design was obtained.