Number of parameter sets generated by latin hyercube sampling In MATLAB, X = lhsdesign(n,p) generates a latin hypercube sample of n number of random parameter sets (n values on each of p variables). By the definition of latin hypercube sampling, there is a much larger number of parameter sets than n that the latin hypercube sample should explore (max. number of parameter sets = n!^(p-1)). Is there a way to set this number of random parameter sets for lhsdesign to generate? or a way for me to visualize all the different parameter sets generated each time I run lhsdesign?
 A: Perhaps to answer your question, it would help to create a small example.  Let's say I want to take a LHS of 4 samples on 2 parameters.  The LHS samples are continuous and uniformly distributed on each margin.
x1, x2
0.1, 0.2
0.4, 0.9
0.7, 0.3
0.8, 0.6

There are an infinite number of unique samples that can be drawn since the samples are stratified simple random samples.  If you consider only the "cell" of the LHS as a unique sample, then there are, as you said, n!^(p-1) different arrangements of cells.  Any one LHS will intentionally only pick one of those arrangements.  The point is that the one LHS with one arrangement of cells is a more efficient sample of the design space than a strictly simple random sample of the same design space of equivalent sample size.  
If you want to iterate through all possible LHS designs, you are essentially conducting an experiment at every design cell location.  You are not gaining any of the efficiency of the LHS design, so that is not normally how LHS algorithms are written.
