one of the easiest ways to construct an lsh family is by bit sampling. this approach works for the hamming distance over d-dimensional vectors formula_49. here, the family formula_1 of hash functions is simply the family of all the projections of points on one of the formula_51 coordinates, i.e., formula_52, where formula_53 is the formula_54th coordinate of formula_55. a random function formula_56 from formula_57 simply selects a random bit from the input point. this family has the following parameters: formula_58, formula_59.