Two‐level factorial designs are widely used in industry. For experiments involving n factors, the construction of designs comprising $2^n$ and $2^{n‐p}$ factorials, arranged in blocks of size $2^q$ is investigated. The aim is to estimate all main effects and a selected subset of two‐factor interactions. Designs constructed according to minimum aberration criteria are shown to not necessarily be the most appropriate designs in this situation. A design construction approach is proposed which exploits known results on proper vertex colourings in graph theory. Examples are provided to illustrate the results and construction strategies. Particular consideration is given to the special case of designs with blocks of size four and tables of designs are given for this block size.

中文翻译：

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构建封闭的因子设计以估计主要影响和选定的两因素相互作用

两级因子设计在工业中被广泛使用。对于涉及n个因子的实验，设计的构建包括$2^{ñ}$ 和 $2^{ñ‐p}$ 阶乘，按大小块排列 $2^q$被调查。目的是估计所有主要影响以及两因素相互作用的选定子集。在这种情况下，根据最小像差标准构造的设计不一定是最合适的设计。提出了一种设计构造方法，该方法利用图论中适当顶点着色的已知结果。提供示例来说明结果和构建策略。特别考虑了具有大小为4的块的设计的特殊情况，并为此块大小提供了设计表。