带可分解性质的组合设计是设计理论的重要研究对象，有着广泛的应用。柯克曼三元系大集（LKTS）问题是组合设计领域中最为著名的公开问题之一。导出设计为Frame的H设计（FDH），不仅自身拥有良好的性质，而且与柯克曼三元系大集有密切联系。本项目拟借助组合学、代数、图论等数学工具系统地研究这两类组合设计，扩大它们的存在性结果。具体而言，LKTS的研究主要针对一些关键小阶数的直接构造并系统研究LKTS的构造方法；FDH的研究主要扩大FDH(v,2,4,3)的直接构造结果并系统研究FDH与LKTS关系。此外，由于涉及大量的计算，设计高效的分布式计算算法也是本项目的一项研究内容。

Resolvable problems are import subjects in combinatorial design theory and have been widely used in many areas. The problem for the existence of large sets of kirkman triple systems (LKTS) is an outstanding open problem in combinatorial design theory. Frame derived H-design(FDH) not only has strong combinatorial properties but also has close relation with LKTS. This project plans to apply combinatorics, algebra, graph theory and other mathematic tools to study two classes of block designs and extends the results. More specifically, the research on LKTS will try to solve the direct construction of some key orders and study the recursive construction systematiclly. The study of FDH focuses on the direct construction of FDH(v,2,4,3) and the relations between LKTS and FDH. In addition, distributed algorithms will be researched to satisfy the large scale computing.