On an explicit lower bound for the star discrepancy in three dimensions

Following a result of D. Bylik and M.T. Lacey from 2008 it is known that there exists an absolute constant η>0 such that the (unnormalized) L∞-norm of the three-dimensional discrepancy function, i.e. the (unnormalized) star discrepancy DN∗, is bounded from below by DN∗≥c(logN)1+η, for all N∈N sufficiently large, where c>0 is some constant independent of N. This paper builds upon their methods to verify that the above result holds with η<1/(32+441)≈0.017357…