Renaissance Packings
Symmetry and structure for practical multidimensional design
Thomas R. Bewley. Published in draft and updated continuously; the PDF below is always the current version.
The elegant field of n-dimensional sphere packings is mature in its mathematical development. However, it is still relatively limited in its practical applications, especially for n > 3. After a brief historical retrospective in §1, the present text first reviews this powerful body of “pure mathematics”, focusing on the construction of dense lattices in §2, and on rare packings and their corresponding nets in §3; the latter chapter includes some useful rare constructions for n > 3 which were apparently not previously known.
From the preface, Renaissance Packings
Chapters.
Each chapter opens the current book at that chapter. Code for the book lives in the Renaissance Repository.
- 1A brief historical retrospective on n-dimensional sphere packings
- 2Dense lattices for n ≤ 24
- 3Rare nonlattice packings and nets for n ≤ 8
- 4Error correcting codes
- 5Grid-based optimization via dense lattices
- 6Computational interconnects via rare nets
- AQuantization to the nearest lattice point
- BMore data on select lattices and nets