区组长为4和6的3-设计  

3-wise Design for Block Sizes of Four and Six

作　　者：王建[1] WANG Jian(Department of General Basic Courses,Nantong Vocational University,Nantong 226007,China)

机构地区：[1]南通职业大学公共教学部,江苏南通226007

出　　处：《南通职业大学学报》2023年第2期64-66,共3页Journal of Nantong Vocational University

基　　金：国家自然科学基金资助项目(11571251)。

摘　　要：t-(v,K,λ)设计是一个关联结构(V,B),满足条件:(1)V是v元点集;(2)B是V的子集族(B中的元素称为设计的区组),且每一个区组b∈B有|b|∈K;(3)V中的任意一个t-元子集恰好出现在λ个区组中。Hanani给出了λ=1时3-(v,{4,6},1)存在的充分必要条件。文章证明3-(v,{4,6},λ)存在的充分必要条件是λv≡0(mod 2),λv(v-1)(v-2)≡0(mod 8)且v≥4。A t-(v,K,λ)design is a pair(V,B)where V is a set of cardinality v,B is a collection of subsets of V(the element in B is called a block)with the property that each b∈B has|b|∈K,and every t-element subset of V happens to be contained in exactlyλof these blocks.When λ=1,Hanani gives a necessary and sufficient condition for 3-(v,{4,6},1).It is proved that a 3-(v,{4,6},λ)exists if and only ifλv≡0(mod 2),λv(v-1)(v-2)≡0(mod 8)and v≥4.

关 键 词：T-设计 3-设计 区组长为4和6 

分 类 号：O157[理学—数学]