Latin hypercube sampling involves dividing the range of each theoretical distribution into N intervals (N = # of samples) and randomly drawing one sample from each of the intervals. This ensures a full coverage of the range of each variable.

This can be summarized as follows:

1) Divide the theoretical distribution into N equally probably intervals

2) Randomly select a cumulative probability from each interval

3) Transform each cumulative probability into a random value from the specified theoretical distribution via the inverse cumulative probability function

4) Randomly pair the values of each variable with all of the other variables. This ignores any correlation structure, that is, all variables are assumed independent.