Two-level parallel flats designs
研究了任意f≥3个平行平面的平行平面设计的一般理论，提出了获取所有不等价设计的混杂频率向量并找出最优设计的方法，适用于构建非正则分数、裂区或随机区组设计。
Regular 2n−p designs are also known as single flat designs. Parallel flats designs (PFDs) consisting of three parallel flats (3-PFDs) are the most frequently utilized PFDs, due to their simple structure. Generalizing to f-PFD with f>3 is more challenging. This paper aims to study the general theory for the f-PFD for any f≥3. We propose a method for obtaining the confounding frequency vectors for all nonequivalent f-PFDs, and to find the least G-aberration (or highest D-efficiency) f-PFD constructed from any single flat. PFDs are particularly useful for constructing nonregular fraction, split-plot or randomized block designs. We also characterize the quaternary code design series as PFDs. Finally, we show how designs constructed by concatenating regular fractions from different families may also have a parallel flats structure. Examples are given throughout to illustrate the results.