The Existence Of Variable Strength Mixed Covering Arrays With K?6

A variable strength mixed covering array M,denoted by VCA(N;t,k,g1g2…gk,C),is a N×k array with the property that M is a mixed covering array of strength t with a sub-mixed covering array C of strength t' where t<t',k>k',t^?k',and k' factors of C come from M.The variable strength mixed covering array is a extended form of the mixed covering array.It has important applications in software tests,the internet,agricultural production and so on.Especially,in the complicated interactions,it can meet the request of variable strength,and it also can save the test time,reduce the costs and the number of tests.One of the most important problems is to determine the optimal bound N when variable strength mixed covering array exists.But this is difficult.There are three chapters in this thesis.In the first chapter,we introduce the defini-tion and the background of variable strength mixed covering array.We list some known conclusions of orthogonal arrays and mixed covering arrays,the constructions and results which we have obtained in this paper.In the second chapter,we give some construc-tions and corollaries of variable strength mixed covering arrays.In the third chapter,we discuss the existence of the optimal variable strength mixed covering arrays of strength t = 2 with a sub-mixed covering array of strength t'=3 when k?6.