Covering aspects of the Niemeier lattices

Adel Alahmadi (1) , Michel Deza (2) , Mathieu Dutour Sikirić (3) , Patrick Sole (4)

1 Department of Mathematics [Jeddah]
2 ENS-PSL - École normale supérieure - Paris
3 Rudjer Boskovic Institute [Zagreb]
4 LAGA - Laboratoire Analyse, Géométrie et Applications

The Niemeier lattices are the 23 unimodular even lattices of norm 2 in dimension 24. We determine computationally their covering radius for 16 of those lattices and give lower bounds for the remaining that we conjecture to be exact. This is achieved by computing the list of Delaunay polytopes of those lattices.

Domaines: Combinatoire [math.CO]

Adel Alahmadi, Michel Deza, Mathieu Dutour Sikirić, Patrick Sole. Covering aspects of the Niemeier lattices. European Journal of Combinatorics, 2019, 80, pp.102 - 106. ⟨10.1016/j.ejc.2018.02.038⟩. ⟨hal-02411614⟩