Thruout these notes three equivalent terms are used with different connotations:
Some standard radius sphere whose center is a lattice point.
The interior of the sphere.
Lattice point
One of a set of isolated points regularly spread thru n dimensional (nD) Euclidean space.
Within a lattice all balls or spheres are the same size.

Notation such as “(28, 016)” means the set of all 24D vectors with 8 twos and 16 zeros. There are 24!/(8!16!) of them.

Code fragments are mostly in the language Scheme and presume this framework.

Original notes
3D packing and nD oblique coördinates
Leech Lattice notes
Computerization of other’s Leech discoveries
Lumps: a Leech Landmark
Simplexes scattered in the Leech Lattice
Buggy notes
which have errors intermixed with some possibly useful stuff