中文摘要：

本文利用差方法对自反MD设计SCMD（4mp，p，1）的存在性给出了构造性证明，这里p为奇素数，m为正整数．

英文摘要：

A Mendelsohn design MD（v,k,λ） is a pair （X,B）, where X is a v-set and B is a collection of k-tuples from X such that each ordered pair from X is contained in exactly A k-tuples of B. An MD（v, k, λ） is called self-converse and denoted by SCMD（v, k, A） = （X,B, f）, if there exists an isomorphic mapping f from （X, B） to （X, B^-1）. In this paper, using difference method, we give a constructive proof for the existence of SCMD（4mp,p, 1）, where p is an odd prime and m is a positive integer.