Discrepancy bounds for a class of negatively dependent random points including Latin hypercube samples

We introduce a class of $\gamma$-negatively dependent random samples. prove that this includes, apart from Monte Carlo samples, in particular Latin hypercube samples and padded by Carlo. For $N$-point sample dimension $d$ we provide probabilistic upper bounds for its star discrepancy with explicitly stated dependence on $N$, $d$, $\gamma$. These generalize the [Heinrich et al., Acta Arith. 96 (2001), 279--302] [C.~Aistleitner, J.~Complexity 27 (2011), 531--540], they are optimal In special case constants appear our improve substantially presented latter paper M.~T.~Hofer, Math. Comp.~83 (2014), 1373--1381].