Optimal Polynomial Tractability Exponents for the Inverse Star Discrepancy

The inverse of the star discrepancy $n^\ast(d, \varepsilon)$ satisfies \[ d \varepsilon^{-1} \lesssim n^{\ast}(d,\varepsilon)\lesssim d\varepsilon^{-2} \] for all $d \in \mathbb{N}$ and $0 < \varepsilon < \varepsilon_0$. The upper bound was established by Heinrich, Novak, Wasilkowski and Woźniakow