Constructing of Multiple-Element Systems with V Order

This paper gives the definitions of exported design and residual design is given. The relation of order between derived design and residual design has been clarified. The blocks capacity in derived design are and the blocks capacity in residual design are . The number of non-isomorphism derived design is equal to the residual design. If the incidience matrix of derived design is , then the incidience matrix of residual design is . The blocks in derived design and the blocks in residual design exist the complementary relationship. The construction methods of derived design and residual design have been proposed. The entire procedure of constructing (15,7,3) derived design and (15,8,2) residual design is also presented completely.