  We prove several results related to a Logvinenko-Sereda type theorem on
dominating sets for generalized doubling Fock spaces. In particular, we give a
precise polynomial dependence of the sampling constant on the relative density
parameter $\gamma$ of the dominating set. Our method is an adaptation of that
used in \cite{HKO} for the Bergman spaces and is based on a Remez-type
inequality and a covering lemma related to doubling measures.
