TY - JOUR
T1 - Covering arrays, augmentation, and quilting arrays
AU - Colbourn, Charles J.
N1 - Funding Information:
The authors are grateful to the referee for his (or her) careful reading and correction, which greatly improved the presentation of the paper. Research supported by KPCME (No. 210243), NSFC (No. 11161046), the TianYuan Special Funds of NSFC (No. 11126113), Xinjiang Young Scientific and technological innovation personnel training project (No. 2013721012).
PY - 2014/9/1
Y1 - 2014/9/1
N2 - Numerous constructions of the best known covering arrays are effective only for specific numbers of symbols. Fusion replaces numerous symbols by one, and can thereby employ such constructions to produce useful covering arrays on fewer symbols. Augmentation instead replaces one symbol by many, permitting the construction of covering arrays from those with fewer symbols. Until this time, augmentation has been of limited value because it introduces substantial redundant coverage. Here a general augmentation method is improved upon by analyzing the classes of interactions to be covered and employing variants of covering arrays, quilting arrays, to reduce the redundancy introduced. For strengths four, five, and six, quilting arrays are produced that can be used in the refined augmentation to produce many best known covering arrays.
AB - Numerous constructions of the best known covering arrays are effective only for specific numbers of symbols. Fusion replaces numerous symbols by one, and can thereby employ such constructions to produce useful covering arrays on fewer symbols. Augmentation instead replaces one symbol by many, permitting the construction of covering arrays from those with fewer symbols. Until this time, augmentation has been of limited value because it introduces substantial redundant coverage. Here a general augmentation method is improved upon by analyzing the classes of interactions to be covered and employing variants of covering arrays, quilting arrays, to reduce the redundancy introduced. For strengths four, five, and six, quilting arrays are produced that can be used in the refined augmentation to produce many best known covering arrays.
KW - Covering array
KW - augmentation
KW - orthogonal array
KW - quilting array
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U2 - 10.1142/S1793830914500347
DO - 10.1142/S1793830914500347
M3 - Article
AN - SCOPUS:85073165428
SN - 1793-8309
VL - 6
JO - Discrete Mathematics, Algorithms and Applications
JF - Discrete Mathematics, Algorithms and Applications
IS - 3
M1 - 1450034
ER -