More mutually unbiased bases
This work introduces an ansatz using tensor products of Fourier and Hadamard matrices to construct more mutually unbiased bases (MUBs) than previously known in many dimensions. The construction yields specific counts, such as five MUBs in dimension 12 and seven in dimension 36, exceeding standard tensor product bounds. Furthermore, a method using Paley's real Hadamard matrix allows for constructing an unbounded number of bases related to prime powers.