Modified Frames With Block Size Four

A holey frame is a holey group divisible design whose blocks can be partitioned intoholey parallel classes, which is powerful for the construction of other types of combina-torial designs. Modified frame is a special case of holey frame that each part owns oneelement, which can be used to construct some other designs such as RGDD,MGDD,semiframe and so on. In this thesis, we shall investigate the existence of modified frameswith block size 4.The thesis is given with four chapters as follows:In Chapter 1, some concepts and results are introduced, such as group divisibledesign, modified frame and so on.In Chapter 2, we give some recursive constructions for modified frames.In Chapter 3, by the necessary condition of modified frame and some direct con-structions we obtain the main conclusions.In Chapter 4, we list some further problems.