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 been established using the Stein-Lovász-Johnson strategy and the Lovász local lemma. A series of improvements on these bounds is developed in this paper. First an estimate for the discrete Stein-Lovász-Johnson bound is derived. Then using alteration, the Stein-Lovász-Johnson bound is improved upon, leading to a two-stage construction algorithm. Bounds from the Lovász 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 Lovász local lemma and the conditional Lovász local lemma distribution.
- Conditional expectation algorithm
- Covering array
- Lovász local lemma
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