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. The unqualified term “neighbor” refers to a ball that touches the ball at the origin.

Notation such as “(28, 016)” means the set of all 24D vectors with 8 twos and 16 zeros. There are 24!/(8!16!) = 735471 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