Unlock: Fast and Sparse Johnson-Lindenstrauss Transforms

Applying a Johnson-Lindenstrauss embedding faster than a dense k-by-d matrix: the Ailon-Chazelle fast transform, the dual BCH and RIP-based refinements, sparse matrices with order log(1/delta)/epsilon nonzeros per column, and the Larsen-Nelson theorem that no embedding, linear or not, beats order log(n)/epsilon^2 dimensions on worst-case point sets.