Kochen-Specker theorem for 8-dimensional space
  A Kochen-Specker contradiction is produced with 36 vectors in a real 8-dimensional Hilbert space. These vectors can be combined into 30 distinct projection operators (14 of rank 2, and 16 of rank 1). A state-specific variant of this contradiction requires only 13 vectors, a remarkably low number for 8 dimensions. 
Michael Kernaghan and Asher Peres