To some extent the purpose of this code is to demonstrate that while the s-box seems like 256 values in random order, it is actually the composition of multiple

To some extent the purpose of this code is to demonstrate that while the s-box seems like 256 values in random order, it is actually the composition of multiple operations in finite field arithmetic. The values in the S-box I would argue are also based on "nothing up my sleeve numbers". The values all depend on the irreducible polynomial and the field size, as well as the specific affine transformation. Knowing the field size and irreducible polynomial, you can then make guarantees about the properties of numbers when transformed using an S-box.