  In this paper we study the relation between two notions of largeness that
apply to a set of positive integers, namely $\mathrm{Nil}_d{-}\mathrm{Bohr}$
and $\mathrm{SG}_k$, as introduced by Host and Kra. We prove that any
$\mathrm{Nil}_d{-}\mathrm{Bohr}_0$ set is necessarily $\mathrm{SG}_k$ where
${k}$ is effectively bounded in terms of $d$. This partially resolves a
conjecture of Host and Kra.
