  A set grading on the split simple Lie algebra of type $D_{13}$, that cannot
be realized as a group-grading, is constructed by splitting the set of positive
roots into a disjoint union of pairs of orthogonal roots, following a pattern
provided by the lines of the projective plane over $GF(3)$. This answers in the
negative Question 1.11 in Elduque-Kochetov monograph (2013).
  Similar non-group gradings are obtained for types $D_n$ with $n$ congruent to
1 modulo 12, by substituting the lines in the projective plane by blocks of
suitable Steiner systems.
