Lattice rules for (hyper)cubic grids

[PaulWAyers]

Among the most efficient ways to integrate of a (hyper)cube are the lattice rules. There are several choices here, but probabilty the embedded lattice rules are the easiest to implement, and they have been tabulated.

For a (simpler) lead reference, I recommend the early paper from Sloan.

It would be good to use lattice rules as an alternative for integration over a cube or (after an affine transformation) an arbitrary parallelepiped. I'm much less sure that higher-dimensions are supported, but it is easy to support arbitrary-dimensional integration on a parallelepiped (beyond $d=3000$, which is more than enough!) with a lattice rule. Interpolation is also relatively straightforward, as it is a generalization of the current structure with specially selected vectors.