On Almost-Uniform Generation of SAT Solutions: The power of 3-wise independent hashing

Given a Boolean formula φ and a distribution parameter ε, the problem of almost-uniform generation seeks to design a randomized generator such that every solution of φ is output with probability within (1 + ε)-factor of where sol(φ) is the set of all the solutions of φ. The prior state of the art scheme due to Jerrum, Valiant, and Vazirani, makes calls to a SAT oracle and employs 2 − wise independent hash functions.