Latin hypercube sampling

The sampling method is often used to construct computer experiments or for Monte Carlo integration.

[1] LHS was described by Michael McKay of Los Alamos National Laboratory in 1979.

A Latin hypercube is the generalisation of this concept to an arbitrary number of dimensions, whereby each sample is the only one in each axis-aligned hyperplane containing it.

sample points are then placed to satisfy the Latin hypercube requirements; this forces the number of divisions,

In two dimensions the difference between random sampling, Latin hypercube sampling, and orthogonal sampling can be explained as follows: Thus, orthogonal sampling ensures that the set of random numbers is a very good representative of the real variability, LHS ensures that the set of random numbers is representative of the real variability whereas traditional random sampling (sometimes called brute force) is just a set of random numbers without any guarantees.