the order 3 magic square appeared in ancient china is the oldest instance for combinatorial design . there also were a large number of examples on magic square in ancient india and arab 出现于中国的3阶幻方是组合设计的最早特例,在印度、阿拉伯等国家对幻方也有较早的研究。
(1 ) state the appearance of block design and it's resolution . ( 2 ) formulate the history of ols ( orthogonal latin squares ) and show the role that euler's conjecture and macneish's conjecture on ols played in the progress of study on latin square . ( 3 ) state briefly the motivation that finite projective plan and finite field offer to the development of combinatorial design (1)详述了18世纪中期提出的区组设计问题以及这些问题出现的多种形式及解决方法;(2)对组合设计中正交拉丁方的历史予以阐述,分析了拉丁方问题的研究中欧拉猜想和麦克奈希猜想的作用;(3)简述了有限射影几何及有限域在组合设计中的意义及其对组合设计理论发展的推动作用。
in this thesis, we first introduce the methodology of combinatorial design of testing parameters and the effectiveness of pairwise testing . then we define pair-combinatorial graph ( pcg ) and case sub graph ( csg ) to analyze the pair-cover problem and indicate that to achieve a minimum test set for pairwise testing is an npc problem, but the size of such test set is in a predictable range 本文首先介绍基于参数组合的测试设计方法和配对覆盖测试方法的有效性,并提出配对组合图(pair-combinatorialgraph,pcg)和案例子图(casesubgraph,csg)的概念来描述配对覆盖问题。