The following methods for constructing space-filling designs are available:
Sphere Packing
Creates a design that maximizes the minimum distance between pairs of design points. The effect of this maximization is to spread the points out as much as possible inside the design region. See Additional Examples of Space Filling Designs and Create the Sphere-Packing Design for the Borehole Data.
Latin Hypercube
Creates a design that maximizes the minimum distance between design points but requires even spacing of the levels of each factor. Each factor has as many levels as there are runs in the design. This method produces designs that mimic the uniform distribution. The Latin Hypercube method is a compromise between the Sphere-Packing method and the Uniform design method. See Example of Creating a Latin Hypercube Design.
Uniform
Creates a design that minimizes the discrepancy between the design points (which have an empirical uniform distribution) and a theoretical uniform distribution. See Example of Creating a Uniform Design. See Fang et.al. (2000) or Hickernell (1998).
Note: These designs are most useful for getting a simple and precise estimate of the integral of an unknown function. The estimate is the average of the observed responses from the experiment.
Minimum Potential
Creates a design that spreads points inside a sphere around the center. Minimum Potential designs have spherical symmetry, are nearly orthogonal, and have uniform spacing. See Example of a Minimum Potential Design.
Maximum Entropy
Creates a design that maximizes The Shannon information of an experiment. See Example of a Constrained Fast Flexible Filling Design.
Gaussian Process IMSE Optimal
Creates a design that minimizes the integrated mean squared error of the Gaussian process over the experimental region. The Gaussian process IMSE optimal design method uses a correlation structure similar to that of the kriging model. See Jones and Johnson (2009).
Note: If the number of runs is 500 or less, a Gaussian Process model is saved to the data table. If the number of runs exceeds 500, a Neural model is saved to the data table.
Fast Flexible Filling
Creates a design using the Fast Flexible Filling algorithm. The algorithm begins by generating a large number of random points within the specified design region. These points are then clustered using a Fast Ward algorithm into a number of clusters that equals the Number of Runs that you specified. The final design points can be obtained by using the default MaxPro (maximum projection) optimality criterion or by selecting the Centroid criterion. See Example of a Constrained Fast Flexible Filling Design and Example of a Constrained Fast Flexible Filling Design. The rows of the design table are automatically randomized.
Note: If you have categorical factors, mixture factors, or factor constraints, then Fast Flexible Filling is the only space filling design method available.