Remember that for MiMC-n/n, d has to satisfy the condition gcd(d, 2^n − 1) = 1 in order to be a permutation, while in the case of MiMC-2n/n (that is, for Feistel Networks) this condition is not necessary.
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Thus, the number of rounds to guarantee the security against the algebraic attacks doesn’t change choosing exponent of the form 2^t + 1 for t > 1. That is, both from the security point of view and from the implementation one, there is no advantage to choose exponents of the form 2^t + 1 greater than 3.
I think it's safe to say that the current exponent 5 can be reduced to 3.
As per §5.3 of https://eprint.iacr.org/2016/492.pdf
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I think it's safe to say that the current exponent
5can be reduced to3.However, there is ambiguity in the MiMC paper...