Almost k-wise independence versus k-wise independence

We say that a distribution over {0,1}ⁿ is (ε,k)-wise independent if its restriction to every k coordinates results in a distribution that is -close to the uniform distribution. A natural question regarding (ε,k)-wise independent distributions is how close they are to some k-wise independent distribution. We show that there exist (,k)-wise independent distributions whose statistical distance is at least n^O(k)· from any k-wise independent distribution. In addition, we show that for any (ε,k)-wise independent distribution there exists some k-wise independent distribution, whose statistical distance is n^O(k)·.