Constructions Of Three-Strength Covering Arrays With Mixed Alphabet Sizes

A mixed covering array of size N,strength t,degree κ;,and type Πik=1vi is a λ×N array with the cells of row i filled with elements from vi,in which t x N subarrays contains every possible t×1column at least once.Since covering arrays have closed relations with software testing,so in recent years,covering arrays has aroused many scholars’s concern and has got much good result.in this paper we construct3-strength,k=3,4,5,6mixed covering arrays and give their upper bounds.Furthermore we use the advanced method to construct the3-strength,k≥7mixed covering array and give their upper bounds.This paper consists of four parts:Section one gives some basic concepts of the covering arrays and a survey of covering arrays.It also contains some symbols which will be used in this paper.Section two give constructions of strength3width3,4,5,6. Some of these covering arrays are optimal in some cases.Section three gives construction of3-strength.width>7mixed covering arrays and give their upper bounds.Section four points out the issues which need to be further study.