In this paper, we show that three-class association schemes can be constructed from certain partial geometric designs. First, we show that partial geometric designs with exactly three indices: $r-n$, ${\lambda }_1$ and ${\lambda }_2$ give rise to three-class association schemes, using the method of Beker and Haemers (1980). Second, we describe parameter sets of certain partial geometric designs that also give rise to three-class association schemes.

中文翻译：

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部分几何设计的三类关联方案

在本文中，我们表明可以从某些局部几何设计中构造三类关联方案。首先，我们显示具有三个指数的部分几何设计：$\mathrm{[R}-ñ$， ${\lambda }_{\mathrm{1个}}$ 和 ${\lambda }_2$运用Beker和Haemers（1980）的方法得出了三级关联方案。其次，我们描述某些局部几何设计的参数集，这些参数集也会产生三类关联方案。