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Upper bounds on the size of covering arrays
- Publication Year :
- 2016
-
Abstract
- Covering arrays find important application in software and hardware interaction testing. For practical applications it is useful to determine or bound the minimum number of rows, CAN$(t,k,v)$, in a covering array for given values of the parameters $t,k$ and $v$. Asymptotic upper bounds for CAN$(t,k,v)$ have earlier been established using the Stein-Lov\'asz-Johnson strategy and the Lov\'asz local lemma. A series of improvements on these bounds is developed in this paper. First an estimate for the discrete Stein-Lov\'asz-Johnson bound is derived. Then using alteration, the Stein-Lov\'asz-Johnson bound is improved upon, leading to a two-stage construction algorithm. Bounds from the Lov\'asz local lemma are improved upon in a different manner, by examining group actions on the set of symbols. Two asymptotic upper bounds on CAN$(t,k,v)$ are established that are tighter than the known bounds. A two-stage bound is derived that employs the Lov\'asz local lemma and the conditional Lov\'asz local lemma distribution.
Details
- Database :
- arXiv
- Publication Type :
- Report
- Accession number :
- edsarx.1603.07809
- Document Type :
- Working Paper