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

Discrepancy Bounds for a Class of Negatively Dependent Random Points Including Latin Hypercube Samples