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Notes on Sphere Packings

Published online by Cambridge University Press:  20 November 2018

John Leech*
Affiliation:
Computing Department, The University of Glasgow
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These notes are to supplement my paper (4), and should be read in conjunction with it. Both are divided into three parts, and in these notes the section numbers have a further digit added; thus §1.41 here supplements §1.4 of (4). References by section numbers are always to (4) or to the present notes, but references to other papers are numbered independently.

The principal results of these notes are the following. New sphere packings are given in [2m], m ⩾ 6, and in [24], which are twice as dense as those of §§1.6, 2.3. Others are given in [2m], m ⩾ 5, with the same density as those of §1.6, but in which each sphere touches fewer other spheres than in the earlier packings.

Type
Research Article
Copyright
Copyright © Canadian Mathematical Society 1967

References

1. Barnes, E. S., The construction of perfect and extreme forms, II, Acta Arith., 5 (1959), 205222.Google Scholar
2. Barnes, E. S. and Wall, G. E., Some extreme forms defined in terms of Abelian groups, J. Austral. Math. Soc., 1 (1959), 4763.Google Scholar
3. Coxeter, H. S. M. and Todd, J. A., An extreme duodenary form, Can. J. Math., 5 (1953), 384392.Google Scholar
4. Leech, J., Some sphere packings in higher space, Can. J. Math., 16 (1964), 657682.Google Scholar
5. Rogers, C. A., Packing and covering (Cambridge 1964).Google Scholar