Thats a unique idea.You should consider the following idea to enhance your idea so that it would impact uniquely:  show that there are constants k,K>0 such that for all N,s@?N, s@?N, the point set consisting of N points chosen uniformly at random in the s-dimensional unit cube [0,1]^s with probability at least 1-e^-^k^s admits an axis-parallel rectangle [0,x]@?[0,1]^s containing KsN points more than expected. Consequently, the expected star discrepancy of a random point set is of order s/N.
['Benjamin Doerr']
I am writing a research paper on a idea A lower bound for the discrepancy of a random point set
[{"from": "human", "value": "I am writing a research paper on a idea A lower bound for the discrepancy of a random point set"}, {"from": "gpt", "value": "Thats a unique idea.You should consider the following idea to enhance your idea so that it would impact uniquely:  show that there are constants k,K>0 such that for all N,s@?N, s@?N, the point set consisting of N points chosen uniformly at random in the s-dimensional unit cube [0,1]^s with probability at least 1-e^-^k^s admits an axis-parallel rectangle [0,x]@?[0,1]^s containing KsN points more than expected. Consequently, the expected star discrepancy of a random point set is of order s/N."}]