TY - JOUR
T1 - Mixed covering arrays of strength three with few factors
AU - Colbourn, Charles
AU - Shi, Ce
AU - Wang, Chengmin
AU - Yan, Jie
N1 - Funding Information:
The authors thank Prof. J. Yin for his helpful comments and suggestions. Ce Shi is supported by NSFC under Grant no. 10831002 . Chengmin Wang is supported by NSFC under Grant no. 10801064 and the Program for Innovative Research Team of Jiangnan University. Jie Yan is supported by NSFC under Grant nos. 10926103, 11001109 .
PY - 2011/11
Y1 - 2011/11
N2 - 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}.
AB - 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}.
KW - Covering array
KW - Mixed covering array
KW - Orthogonal array
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U2 - 10.1016/j.jspi.2011.05.018
DO - 10.1016/j.jspi.2011.05.018
M3 - Article
AN - SCOPUS:79959780043
SN - 0378-3758
VL - 141
SP - 3640
EP - 3647
JO - Journal of Statistical Planning and Inference
JF - Journal of Statistical Planning and Inference
IS - 11
ER -