  In order to describe the right setting to handle Zauner's conjecture on
mutually unbiased bases (MUBs) (saying that in $\mathbb{C}^d$, a set of MUBs of
the theoretical maximal size $d + 1$ exists only if $d$ is a prime power), we
pose some fundamental questions which naturally arise. Some of these questions
have important consequences for the construction theory of (new) sets of
maximal MUBs.
