In this paper, we focus on partial geometric designs with block sizes three and four. First, we show that a partial geometric design with block size three is a 2‐design, or a transversal design, or each line of a generalized quadrangle that is repeated $\lambda$ times. Second, we introduce the concept of type of partial geometric designs with block size four and characterize partial geometric designs of type $\left[\lambda ,1,1\right]$ for some integer $\lambda \ge 1$.

中文翻译：

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块大小为3和4的部分几何设计

在本文中，我们专注于块大小为三个和四个的部分几何设计。首先，我们证明块大小为3的局部几何设计是2设计或横向设计，或者是重复的广义四边形的每条线$\lambda$时代。其次，我们介绍块大小为4的部分几何设计的类型的概念，并描述类型为的部分几何设计的特征$\left[\lambda ，\mathrm{1个}，\mathrm{1个}\right]$ 对于一些整数 $\lambda \ge \mathrm{1个}$。