Mutually Unbiased Bases and Finite Projective Planes
  It is conjectured that the question of the existence of projective planes whose order is not a power of prime is intimately linked with the problem whether there exists a set of d+1 mutually unbiased bases in a d-dimensional Hilbert space if d differs from a power of prime. 
Metod Saniga, Michel Planat, Haret Rosu