I am also interested in generating a special type of Latin hypercube called a symmetric Latin hypercube. Concatenating these together into a DxN matrix gives a list of coordinates which will form a Latin hypercube. One algorithm for generating this is to generate D random permutations of the integers 0 through N-1, where D is the number of dimensions and N is the desired number of samples. e.g., for 2 dimensions and 4 total samples, this is a Latin hypercube: | | | |x| Latin hypercubes are essentially collections of points on a hypercube that are placed on a cubic/rectangular grid, which possess the property that no two points share any individual coordinate, and every row/column/higher-dimensional-axis is sampled once. I wrote some code to generate Latin hypercube samples for interpolation over high-dimensional parameter spaces.
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