Generalised Hermite constants and designs

Bertrand Meyer, CWI

The generalised Hermite constant accounts for the size of the biggest minimal sub-structure one can find in a lattice of a given dimension (e.g. the minimal length of a nonzero lattice vector or the minimal volume of its sublattices of fixed dimension). We shall show how to characterize the lattices that locally achieve the constant in the spirit of Voronoi work and develop a technique based on representation theory and designs to exhibit such examples.

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