see

Neural network based modeling of HfO2 thin film characteristics using Latin Hypercube Sampling

Kyoung Eun Kweon, Jung Hwan Lee, Young-Don Ko, Min-Chang Jeong, Jae-Min Myoung, Ilgu Yun

https://booksc.xyz/book/3077927/aeb672

With Boolean variables. Assuming a 4x4x4x4 Latin Hypercube (4 factors and 4 treatments) you can use,

y=b0+b1x1+b2x2+b3x3+ c1w1+c2w2+c3w3+ d1z1+d2z2+d3z3+ e1u1+e2u2+e3u3+

f1v1+f2v2+f3v3

where

x1=[1 if response is from treat A, 0 otherwise]

x2=[1 if response is from treat B, 0 otherwise]

x3=[1 if response is from treat C, 0 otherwise]

w1=[1 if response is form 1 level of factor 1, 0 otherwise]

w2=[1 if response is form 2 level of factor 1, 0 otherwise]

w3=[1 if response is form 3 level of factor 1, 0 otherwise]

z1=[1 if response is form 1 level of factor 2, 0 otherwise]

z2=[1 if response is form 2 level of factor 2, 0 otherwise]

z3=[1 if response is form 3 level of factor 2, 0 otherwise]

u1=[1 if response is form 1 level of factor 3, 0 otherwise]

u2=[1 if response is form 2 level of factor 3, 0 otherwise]

u3=[1 if response is form 3 level of factor 3, 0 otherwise]

v1=[1 if response is form 1 level of factor 4, 0 otherwise]

v2=[1 if response is form 2 level of factor 4, 0 otherwise]

v3=[1 if response is form 3 level of factor 4, 0 otherwise]

and you can calculate the parameters b0, b1, b2,…, f3 by multiple linear regression with Mathematica, Mat-Lab, or Excel.

Is there a specific requirement for Mathematica? It is know that this software is more useful for symbolic manipulation, rather than numerical calculation. There is a spectrum of codes out there that will teach you LHS. In itself, the baseline algorithm is straightforward. Its efficient implementation is also not so difficult to grasp assuming enough time is spent on it.