@article{Conway1982TheCR,
title={The covering radius of the Leech lattice},
author={John H. Conway and Richard Parker and N. J. A. Sloane},
journal={Proceedings of the Royal Society of London. A. Mathematical and Physical Sciences},
year={1982},
volume={380},
pages={261 - 290}
}

Proceedings of the Royal Society of London. A. Mathematical and Physical Sciences

We investigate the points in 24-dimensional space at maximum distance from the Leech lattice, i. e. the ‘deepest holes’ in that lattice. The maximum distance of any such point from the Leech lattice is shown to be 1/√2 times the minimum distance between the lattice points. Furthermore there are 23 types of ‘deepest hole’, one for each of the 23 even unimodular 24-dimensional lattices found by Niemeier.

BIOGRAPHICAL MEMOIRS OF FELLOWS OF THE ROYAL SOCIETY

2021

John Conway was without doubt one of the most celebrated British mathematicians of the last half century. He first gained international recognition in 1968 when he constructed the automorphism group… Expand

Proceedings of the Royal Society of London. A. Mathematical and Physical Sciences

1982

In this paper a bound is obtained for the covering radius of the Leech lattice that is close to the subsequently obtained true value, by a method which may have more general use.

[-5, 6] promises to be the subject of many investigations. We give here a short proof that this lattice is characterised by some of its simplest properties. Although we must quote two theorems to… Expand

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… Expand