Generates a densest packing-based maximum projection design.
DPMPD(p,n,rotation="magic",w=100)The value returned from the function is a list containing the following components:
The generated design.
The projective separation distance of the generated design, from one-dimensional projections to the unprojected design.
Number of dimensions, must be an integer greater than one and no higher than eight.
Number of points, must be an integer greater than one.
Optional, whether to use magic rotation matrices (for p=2,3,4,6,8, recommended) or random rotation matrices.
Number of rotation matrices to try.
This function generates a densest packing-based maximum projection design in two to eight dimensions. For p=2,4,8 with rotation="magic", the designs are generated following the Biometrika paper "Lattice-based designs possessing quasi-optimal separation distance on all projections". For p=3,6 with rotation="magic", the designs are generated following the arXiv paper "Lattice-based designs with quasi-uniform projections". For other p or rotation!="magic", the designs are generated from random rotations.
He, Xu (2021). "Lattice-based designs possessing quasi-optimal separation distance on all projections", Biometrika, 108(2): 443-454.
He, Xu (2018). "Lattice-based designs with quasi-uniform projections", arXiv:1709.02062v2.