Special cases are summarized in the following table.
The automorphism group has order
giving the first few terms as 2, 8, 1152, 696729600, 89181388800, 48126558103142400, ... (OEIS A014116).
The 16-dimensional Barnes-Wall lattice can be constructed from the Leech lattice .
The generating function of the theta series for the lattice for various orders are summarized in the following table.
|theta series generating function|
The following table gives the theta series themselves.