区组大小为 4 的二重超单可分解的可分组设计

自 1992 年 Gronau 和 Mullin 提出超单设计的概念以来, 很多研究者参与了超单设计的研究. 超单设计在编码等方面也有广泛的应用. 超单可分组设计是超单设计的重要组成部分. 本文我们主要研究区组大小为4 的二重超单可分解的可分组设计, 并基本解决了此类设计的存在性问题.

Super-simple resolvable group divisible designs with block size 4 and index 2

The concept of super-simple designs was first introduced by Gronau and Mullin in 1992. The existence of super-simple designs is an interesting extremal problem by itself, but there are also some useful applications. Super-simple group divisible designs are useful for the construction of other types of super-simple designs. In this paper, we shall show that the necessary conditions for the existence of a super-simple (4,2)-RGDD of type gu are also sufficient possibly except for (g,u) = (12t,27), where t = 2 ...