The space filling designs are primarily intended for computer experiments (simulations) without a stochastic element. The goal is to obtain data of sufficient density to support an interpolator. Is that case your situation? These designs can be used for other purposes, though. These design methods are for continuous factors. The exception is the Fast Flexible Filling method but even it requires at least one continuous factor.
The minimum number of runs is determined by the number of parameters to be estimated in the model. A design with the minimum number of runs is saturated. You will have enough data to estimate all the parameters but none to test the estimates or model as a whole. A custom design requires 8 runs for the main effects model and 18 for the interaction model. I would not recommend a saturated design in most cases.
Can you eliminate any factor levels a priori?
