As the title might suggest, I am referring to this paper https://www.cs.umd.edu/~srin/PDF/ch-bounds.pdf , titled : Chernoff-Hoeffding Bounds for Application with Limited Independence.
The theorem in question is Theorem 5 of the paper, specifically the following
If I wish to reduce back to the generic CH-bound, I would then set $k = n$, where $n$ is the number of $r.v$. But now base on the theorem, I could (potentially) get a better bound than the generic CH-bound. I feel like I am misunderstanding some nuances involving this theorem.
Any help or insight is deeply appreciated
Cheers