Convergence of random sample vs. Latin Hypercube Sampling Latin Hypercube Sampling, by concept, should be able to yield convergence of an estimate of output at a lower number of samples than random sampling. With the model I am working on, I'm continuously seeing convergence happen at a smaller sample size for random sampling than LHS. I was wondering if there would be any possible explanation for this observation. Thank you. 
 A: This behaviour is technically possible but very unusual. I would check your code very carefully to make sure there are no errors in your implementation of the sampling, or perhaps do some more reps to get a fuller understanding of the situation.
Proposition 10.4 in this book chapter, and the discussion below the proposition, might be relevant. The proposition states that, if $f$ is a real-valued function on $[0,1]^d$, $\mu=\int f(x) \,dx$, $\sigma^2=\int (f(x)-\mu)^2\, dx<\infty$, then the variance of the associated LHS estimator $\hat{\mu}_{LHS}=\frac{1}{n}\sum_{i=1}^n f(X_i)$ satisfies $\text{Var}(\hat{\mu}_{LHS})\leq \frac{\sigma^2}{n-1}$. This means that LHS cannot be worse than IID sampling with a sample size of one less (in terms of the variance of the estimator). LHS will tend to do less well for functions $f$ that are far from being additive (in a sense defined in section 10.3 of the book chapter).
There's also a theorem in the paper A Comparison of Three Methods for Selecting Values of Input Variables in the Analysis of Output from a Computer Code by McKay, Beckman and Conover (Technometrics 21:239-245) which states that, if $f$ is monotonic in each of its arguments, then  $\text{Var}(\hat{\mu}_{LHS})\leq \frac{\sigma^2}{n}$ i.e. LHS is never worse than IID sampling.
