The existence of resolvable mendelsohn design RMD({4,s*}, v)

Abstract

The problem we study in this article is the existence of resolvable Mendelsohn design RMD({4,s^*},v), which requires all blocks to be of size 4, except that, each parallel class should contain one block of size s.If s = 4, it is RMD(ν, 4,1).In this article, We shall firstly construct RMD(12,4,1) to completely settle the existence of RMD(ν,4,1), then we shall show the necessary conditions for the existence of RRMD({4,s^*}, v) are sufficient, for the case s = 8,10.