We study lower bounds for Locality Sensitive Hashing (LSH) in the strongest setting: point sets in \{0,1\}^d under the Hamming distance. Recall that \mathcal{H} is said to be an (r, cr, p, q)-sensitive hash family if all pairs x,y \in \{0,1\}^d with dist(x,y) \leq r have probability at least p ... more >>>