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, $\mathsf{CAN}(t,k,v)$, in a covering array for given values of the parameters $t,k$, and $v$. Asymptotic upper bounds for $\mathsf{CAN}(t,k,v)$ have been established using the Stein--Lovasz--Johnson strategy and the Lovasz local lemma. A series of improvements on these bounds is developed in this paper. First an estimate for the discrete Stein--Lovasz--Johnson bound is derived. Then using alteration, the Stein--Lovasz--Johnson bound is improved upon, leading to a two-stage construction algorithm. Bounds from the Lovasz local lemma are improved upon in a different manner, by examining group actions on the set of symbols. Two asymptotic upper bounds on $\mathsf{CAN}(t,k,v)$ are established that are tighter than the known bounds. A two-stage bound is derived that employs the Lovasz local lemma and the conditional Lovasz local lemma ...
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