I'm trying to generate a design of experiments for fitting a response surface for a quantity $Y$ such that, $Y = f(X_1, ..., X_6)$. I'm open to a factorial design as well as a random design. $X_1,..., X_5$ are continuous valued with specified upper bound and lower bound values however, $X_6$ variable is discrete valued. It can only take integer values between 1 and 30.
How do I generate a design of experiments considering the fact that $X_6$ needs to be discrete valued?
I need a second order response surface i.e. there will be interaction terms of the input random variables. Therefore, a simple full factorial wouldn't fit my requirements.
For e.g., consider the case of a central composite design (CCD) for two variables, $X_1$ and $X_6$.
array([[-0.70710678, -0.70710678], [ 0.70710678, -0.70710678], [-0.70710678, 0.70710678], [ 0.70710678, 0.70710678], [ 0. , 0. ], [ 0. , 0. ], [ 0. , 0. ], [ 0. , 0. ], [-1. , 0. ], [ 1. , 0. ], [ 0. , -1. ], [ 0. , 1. ], [ 0. , 0. ], [ 0. , 0. ], [ 0. , 0. ], [ 0. , 0. ]])
Let lower bound of $X_1$ be $2.3$ and upper bound be 2.7. Therefore, -0.707 value for $X_1$ will be 2.358 and 0.707 value will be 2.641. These numbers make sense to my model. However, I don't get how can I get the corresponding values for $X_6$ where -1 corresponds to 1 and +1 corresponds to 30.
Alternatively, can this be done using a randomized design like Latin Hypercube Sampling?