A o(n) monotonicity tester for Boolean functions over the hypercube

A Boolean function $f:\{0,1{\}}^n\mapsto \{0,1\}$ is said to be $\text{eps}$-far from monotone if $f$ needs to be modified in at least $\text{eps}$-fraction of the points to make it monotone. We design a randomized tester that is given oracle access to $f$ and an input parameter $\text{eps}>0$, and has the following guarantee: It outputs {\sf Yes} if the function is monotonically non-decreasing, and outputs {\sf No} with probability $>2\mathrm{/}3$, if the function is $\text{eps}$-far from monotone. This non-adaptive, one-sided tester makes $O(n^{7\mathrm{/}8}{\text{eps}}^{-3\mathrm{/}2}\ln (1\mathrm{/}\text{eps}))$ queries to the oracle.