2016/03/25 by Sarkar, Kaushik, Colbourn, Charles J. · 2 citations
#05A18 #05B30 (primary) #05D99 #62K05 #68P10 (secondary) #Combinatorics (math.CO) #FOS: Mathematics
paper · doi:10.48550/arxiv.1603.07809
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-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.