Thats a unique idea.You should consider the following idea to enhance your idea so that it would impact uniquely: 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.
['Kaushik Sarkar', 'Charles J. Colbourn']
I am writing a research paper on a idea Upper bounds on the size of covering arrays
[{"from": "human", "value": "I am writing a research paper on a idea Upper bounds on the size of covering arrays"}, {"from": "gpt", "value": "Thats a unique idea.You should consider the following idea to enhance your idea so that it would impact uniquely: 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."}]