Abstract Simple nontrivial s -resolvable t -designs for t ≥ 3 and 1 s t are still very sparsely investigated up to now. The problem has been tackled in a recent paper by the author. Here, we continue to explore the problem by focussing on the case t = 3 and s = 2 . In 1963 Shrikhande and Raghavarao published a recursive construction for BIBD. Different authors have studied generalizations of the method for constructing simple 3-designs. In this paper we show that the method can be further extended to studying simple 3-designs having 2-resolutions. As a result, we are able to construct many new infinite families of simple 2-resolvable 3-designs.

中文翻译：

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在具有 2 分辨率的简单 3 设计上

摘要 迄今为止，对 t ≥ 3 和 1 st 的简单非平凡 s 可解析 t 设计的研究仍然很少。作者在最近的一篇论文中已经解决了这个问题。在这里，我们通过关注 t = 3 和 s = 2 的情况继续探索该问题。1963 年，Shrikhande 和 Raghavarao 发表了 BIBD 的递归构造。不同的作者研究了构造简单 3 设计的方法的概括。在本文中，我们表明该方法可以进一步扩展到研究具有 2 分辨率的简单 3 设计。因此，我们能够构建许多新的无限简单 2-可解析 3-设计族。