實驗設計在工業，醫學，農業上已被廣泛的使用，而尋找最佳之實驗配置也一直是實驗設計重要的課趣。為了測試各處理間之差異，不同評定原則下之最佳設計，在各統計文獻中已多論及。其中含有對照處理之問題又是相當常見，例如:在農業上，我們一直使用某種肥料，若有數種新的肥料被發現，且其可能對於收成有更大的助益，則我們必須做一實驗，分析其結果，然從做一決策以決定新的肥料可否取代原來一直接使用之肥料。而在很多實驗的情形下，實驗者必須利用集區來降低誤差，與增加準確性。所以考慮在集區設計與行列設計之實驗下，如何做實驗配置才可得到最佳設計，正是本文探討的主題。

我們將考慮在集區設計與行列設計之實驗中ν個實驗處理與一對照處理間之比較，而本文的目的就是要決定一最佳設計，也就是如何配置此ν+ 1個處理，使得在比較實驗處理與對照處理時所得之估計值變異最小，我們將引用Jacroux and Majumdar (1989)中之不等式去證明並得到一些最佳A型集區設計。且利用Jacroux (1986) 之定理與上述之最佳A型集區設計來推廣而證明且得到一些最佳A型行列設計。其中，我們將利用陳武強(1990) 之”猜測”中使用拉丁方格所建立之某些最佳A型行列設計。

最後，介紹一些我們所得到的最佳A 型設計之建立方式，並舉出一些實例。

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