A distribution $D$ on $\{0,1\}^n$ is $k$-wise independent if any $k$ of the underlying $n$ random variables are independent and each is uniformly distributed. To me this looks similar in spirit to $D$ having $\textit{min-entropy}$ $k$.

Is there any formal relation between $k$-wise independence of a distribution and its min-entropy?

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    $\begingroup$ $k$-wise independence implies the min-entropy is at least $k$. on the other hand it's pretty easy to come up with distributions that are nowhere near $k$-wise independent and have min entropy $k$. $\endgroup$ Mar 7 '15 at 2:49

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