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A Boolean function $f:\{0,1\}^d \mapsto \{0,1\}$ is unate if, along eachcoordinate, the function is either nondecreasing or nonincreasing. In thisnote, we prove that any nonadaptive, one-sided error unateness tester must make$\Omega(\frac{d}{\log d})$ queries. This result improves upon the$\Omega(\frac{d}{\log^2 d})$ lower bound for the same class of testers due toChen et al. (STOC, 2017).

A Lower Bound for Nonadaptive, One-Sided Error Testing of Unateness of Boolean Functions over the Hypercube