  Spurred by the influential work of Viola (Journal of Computing 2012), the
past decade has witnessed an active line of research into the complexity of
(approximately) sampling distributions, in contrast to the traditional focus on
the complexity of computing functions.
  We build upon and make explicit earlier implicit results of Viola to provide
superconstant lower bounds on the locality of Boolean functions approximately
sampling the uniform distribution over binary strings of particular Hamming
weights, both exactly and modulo an integer, answering questions of Viola
(Journal of Computing 2012) and Filmus, Leigh, Riazanov, and Sokolov (RANDOM
2023). Applications to data structure lower bounds and quantum-classical
separations are discussed.
