Kahlerian K3 surfaces and Niemeier lattices
  Using results (especially see Remark 1.14.7) of our paper "Integral symmetric bilinear forms and some of their applications", 1979, we clarify relation between Kahlerian K3 surfaces and Niemeier lattices. We want to emphasise that all twenty four Niemeier lattices are important for K3 surfaces, not only the one which is related to the Mathieu group. 
Viacheslav V. Nikulin
math.AG