在實驗設計的研究中，設計完整列舉與同構檢驗是兩項很困難的工作。雖然這是兩項不同的工作，但彼此之間卻有很密切的關係。設計完整列舉是指生成所有不同構的設計，如所有的正規設計或所有的直交陣列等。而同構檢驗則是比較兩個設計是否可經由行列或是水準互換而得到相同結構。在列舉所有的設計時，經常在某階段需要透過同構檢驗來減少多餘的計算。本篇論文包含兩個主要的部份。在第一個部份，我們基於指標函數和投影理論，提出一個組裝法來列舉所有的兩水準設計。此組裝法利用一個層級的結構而逐步地生成所有的設計。我們亦對此組裝法發展了一個演算法，來完整地生成所有非同構的設計。在第二個部份，我們提出利用計數向量的同構檢驗法。我們亦證明了此方法比文獻中曾提出的許多同構檢驗法更有效率。我們亦使用設計投影的技巧來更進一步改善檢驗的效率。

Design enumeration and isomorphism examination are two difficult tasks in the study of experimental design. The two tasks are different but often related to each other. Design enumeration is concerned with the complete generation of certain types of designs, such as regular designs or orthogonal arrays. Isomorphism examination, on the other hand, compares whether two designs have the same structure subject to some row and column operations. During the process of design enumeration, it is often required to perform isomorphism examination at some stage to reduce the possible redundant calculation. This dissertation includes two main parts. In the first part, we propose an assembly method based on the indicator function and the projection to enumerate all non-isomorphic two-level designs. The assembly method allows us to generate all designs sequentially in a hierarchical structure. We present an algorithm based on the assembly method and generate a complete catalogue of non-isomorphic designs for some cases. In the second part, we develop an initial screening method based on the counting vector for isomorphism examination. We prove that the method provides a more efficient examination than some methods proposed in other articles. The technique of projection is also applied to improve the examination efficiency.

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