Glued lattices are better quantizers than K 12

• 40 years ago, Conway and Sloane proposed using the highly symmetrical Coxeter–Todd lattice K 12 for quantization, and estimated its second moment. Since then, all published lists identify K 12 as the best 12-dimensional lattice quantizer. Surprisingly, K 12 is not optimal: we construct two new 12-dimensional lattices with lower normalized second moments. The new lattices are obtained by gluing together products of two 6-dimensional lattices.

Subject headings

NATURVETENSKAP  -- Matematik -- Sannolikhetsteori och statistik (hsv//swe)

NATURAL SCIENCES  -- Mathematics -- Probability Theory and Statistics (hsv//eng)

Keyword

Block codes

vector quantization

moment of inertia

glue vectors

Reflection

normalized second moment

Voronoi region

quantization constant

Generators

Physics

Lattices

Coxeter–Todd lattice

gluing theory

mean square error

product lattice

Symmetric matrices

Vectors

lattice theory

quantization error

Publication and Content Type

art (subject category)

ref (subject category)