项鸣晓^1，*， 靳贻良^2，

（  1、宁波大学；       2、宁波大学理学院；  ）

摘要： 令v为正整数和K是正整数集合， Mendelsohn设计记为 是对集 ，其中X是v个点的集合，B是X的循环有序子集，大小为集合K（称为区组）使得X中的每一有序对在区组集B中的一个区组中恰只连续出现一次。如果对所有的t=1，2，…r，X中的每一有序对在区组集B中的一个区组中恰是t-分离的，那么 称为r-重完美设计，简记为r-重完美 。如果 和 ，那么r-重 就为 完美Mendelsohn设计，简记为 。在这篇文章中我们来研究区组大小为8，对 且 的完美Mendelsohn设计的存在性。
关键词： （v,k,1）-PMD, BIBD，截态设计TD，Mendesohn 设计

Xiang Mingxiao^1,*， Jin Yiliang^2,

（  1、NingBo university；       2、NingBo University；  ）

Abstract： Let v be a positive integer and let K be a set of positive integers. A (v, K, 1) -Mendelsohn design, which we denote briefly by (v, K, 1) -MD, is a pair (X,B) where X is a v-set and B is a collection of cyclically ordered subsets of X (called blocks) with sizes in the set K such that every ordered pair of points of X are consecutive in exactly one block of B. If for all t=1,2,…,r, every ordered pair of points of X are t-apart in exactly one block of B then the (v, K, 1 ) -MD is called an r-fold perfect design and denoted briefly by an r-fold perfect (v, K, 1 ) -MD. If K = k and r = k-1 ,then an r-fold perfect (v, k, 1-MD is essentially the more familiar (v, k,1) - perfect Mendelsohn design, which is briefly denoted by (v,k,1) -PMD. In this paper, we investigate the existence of pefect Mendelsohn designs with block size 8 and , .

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