Stack Exchange network consists of 183 Q&A communities including Stack Overflow, the largest, most trusted online community for developers to learn, share their knowledge, and build their careers.
I think we have to use Harper's theorem somehow, because the upper-bound we are looking for on $|X|$, is same as the cardinality of a sphere of radius $m/4$ that is less than $2^{0.81m}$
The $1/2$ is not a typo I think. But it is trivial to prove this for $\delta = 1/10$ . The cited reference is a 1966 paper by Kleitman, but I am having trouble using the results there to prove this.
