Constructing of Multiple-element Systems with v Order

摘要

This paper gives the definitions of (v,k,λ) exported design and (v,v-k,v-2r + λ) residual design is given.The relation of order between (v,k,λ) derived design and (v,v-k,v-2r+λ) residual design has been clarified.The blocks capacity in (v,k,λ) derived design are k and the blocks capacity in (v,v-k,v-2r + λ) residual design are v-k.The number of non-isomorphism (v,k,λ) derived design is equal to the (v,v-k,v-2r+λ) residual design.If the incidience matrix of (v,k,λ) derived design is A,then the incidience matrix of (v,v-k,v-2r+λ) residual design is Jvxk-A.The blocks in (v,k,λ)derived design and the blocks in (v,v-k,v-2r+λ) residual design exist the complementary relationship.The construction methods of (v,k,λ) derived design and (v,v-k,v-2r+λ) 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.