Mean king's problem with mutually unbiased bases and orthogonal Latin   squares
  The mean king's problem with maximal mutually unbiased bases (MUB's) in general dimension d is investigated. It is shown that a solution of the problem exists if and only if the maximal number (d+1) of orthogonal Latin squares exists. This implies that there is no solution in d=6 or d=10 dimensions even if the maximal number of MUB's exists in these dimensions. 
A.Hayashi, M.Horibe, and T.Hashimoto