On Sublattices of the Hexagonal Lattice

M. Bernstein(*), N. J. A. Sloane(**), and Paul E. Wright(***)

Mathematical Sciences Research Center 
AT&T Bell Laboratories 
Murray Hill, NJ 07974 USA 

(*)Present address:
Mathematics Department
Univ. California Berkeley
887 Evans Hall
Berkeley CA 94720-3840
Email: mira@math.berkeley.edu

(**)Present address:
Information Sciences Research
AT&T Shannon Lab
Florham Park, NJ 07932-0971 USA
Email: njas@research.att.com

(***)Present address:
120 Potomac Drive
Basking Ridge
NJ 07920


Abstract

How many sublattices of index N are there in the planar hexagonal
lattice? Which of them are the best from the point of view of packing
density, signal-to-noise ratio, or energy? We answer the first question
completely and give partial answers to the other questions.


For the full version see
http://www.research.att.com/~njas/doc/paul.pdf (pdf) or
http://www.research.att.com/~njas/doc/paul.ps (ps)


This paper was published (in a somewhat different form) in
Discrete Math., Vol. 170 (1997), 29-39.