On negative dependence properties of Latin hypercube samples and scrambled nets

We study the notion of γ-negative dependence random variables. This is a relaxation negative orthant (which corresponds to 1-negative dependence), but nevertheless it still ensures concentration measure and allows use large deviation bounds Chernoff-Hoeffding- or Bernstein-type. variables based on points P. These appear naturally in analysis discrepancy P or, equivalently, suitable worst-case integration error quasi-Monte Carlo cubature that uses as nodes. introduce correlation number, which smallest possible value γ dependence. prove interest Latin hypercube sampling (t,m,d)-nets do, general, not have number 1, i.e., they are dependent.