This paper explores the use of maximin Latin hypercube (MmLh) designs for computational experiments, particularly in the context of deterministic function approximation. The authors aim to find designs that balance the maximin distance criterion, which is motivated by Bayesian function prediction, with good projective properties in each dimension, as guaranteed by Latin hypercubes. They introduce a criterion function, $\phi_p$, and a simulated annealing algorithm to construct these designs. The algorithm starts with a random Latin hypercube design and iteratively improves it by perturbing the design and accepting the perturbation with a probability that depends on the improvement in the $\phi_p$ criterion. The paper presents a catalog of MmLh designs for different values of $n$ and $k$, and discusses their geometric properties, particularly for $k = 2$, $n = k$, and $n = 2k$. The designs are found to have interesting geometric properties, such as being approximately equidistant from the center of the region in one-dimensional projections. The authors conclude that MmLh designs can be effective for predicting the output of computer models, especially when only a few inputs are important.This paper explores the use of maximin Latin hypercube (MmLh) designs for computational experiments, particularly in the context of deterministic function approximation. The authors aim to find designs that balance the maximin distance criterion, which is motivated by Bayesian function prediction, with good projective properties in each dimension, as guaranteed by Latin hypercubes. They introduce a criterion function, $\phi_p$, and a simulated annealing algorithm to construct these designs. The algorithm starts with a random Latin hypercube design and iteratively improves it by perturbing the design and accepting the perturbation with a probability that depends on the improvement in the $\phi_p$ criterion. The paper presents a catalog of MmLh designs for different values of $n$ and $k$, and discusses their geometric properties, particularly for $k = 2$, $n = k$, and $n = 2k$. The designs are found to have interesting geometric properties, such as being approximately equidistant from the center of the region in one-dimensional projections. The authors conclude that MmLh designs can be effective for predicting the output of computer models, especially when only a few inputs are important.