Nikolov-Ullman Pure-DP Query Release Conjecture

Nikolov and Ullman asked, as Open Problem 1 on DifferentialPrivacy.org, whether $k$ statistical queries over a universe of size $T$ can be released under pure differential privacy at the square-root error rate that the known lower bounds suggest, rather than the cube-root rate of the classical small-database method. They can: for every $n$ and $\varepsilon > 0$ there is an $\varepsilon$-differentially private mechanism with expected error $O(\min\{1, \sqrt{\log(2T)\log(2k)/(\varepsilon n)}\})$.