What is the best modelling of sequence so we can get any binary elements in our sequences?

For example:

to get sequence 1,0,1,0,1,0,1,0 we may assume our domain is Z23 i.e., {0,1}3, function is f(x1,x2)=1+x1 and range is Z2.

We can consider domain as products of finite fields. We are free to assume any degree polynomial and number of variables.

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