Space-filling designs were developed to provide sufficiently dense data for estimating a flexible interpolator such as a Gaussian process for a highly non-linear response in a computer experiment. These designs have also been successfully used in some cases of formulations to create a mixture design. The search algorithms used by space-filling designs are described here. The algorithm and its options determines the number of runs.

We generally use custom design for fitting a linear statistical model. (Note that it might include terms for non-linear effects in the response.)

On the other hand, if you want to estimate the parameters for a non-linear function as is often the case with kinetics problems, JMP also has a non-linear design platform. You can read about it here.

Why did you choose a space-filling design in the first place?

Learn it once, use it forever!