Mixed covering arrays of strength three with few factors

Charles Colbourn, Ce Shi, Chengmin Wang, Jie Yan

Research output: Contribution to journalArticlepeer-review

4 Scopus citations


Covering arrays with mixed alphabet sizes, or mixed covering arrays, are useful generalizations of covering arrays that are motivated by software and network testing. Suppose that there are k factors, and that the ith factor takes values or levels from a set Gi of size gi. A run is an assignment of an admissible level to each factor. A mixed covering array, MCA(N;t,k,g1g2...gk), is a collection of N runs such that for any t distinct factors, i1,i2,...,it, every t-tuple from Gi1×Gi2×. .×Git occurs in factors i1,i2,...,it in at least one of the N runs. When g=g1=g2=...=gk, an MCA(N;t,k,g1g2...gk) is a CA(N;t,k,g). The mixed covering array number, denoted by MCAN(t,k,g1g2...gk), is the minimum N for which an MCA(N;t,k,g1g2...gk) exists. In this paper, we focus on the constructions of mixed covering arrays of strength three. The numbers MCAN(3,k,g1g2...gk) are determined for all cases with k∈{3,4} and for most cases with k∈;{5,6}.

Original languageEnglish (US)
Pages (from-to)3640-3647
Number of pages8
JournalJournal of Statistical Planning and Inference
Issue number11
StatePublished - Nov 2011


  • Covering array
  • Mixed covering array
  • Orthogonal array

ASJC Scopus subject areas

  • Statistics and Probability
  • Statistics, Probability and Uncertainty
  • Applied Mathematics


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