Realization of saturated transfer systems on cyclic groups of order $p^n{q}^m$ by linear isometries $N_{\mathrm{\infty }}$-operads

We prove a new case of Rubin’s saturation conjecture about the realization of $G$-transfer systems, for $G$ a finite cyclic group, by linear isometries $N_{\mathrm{\infty }}$-operads, namely the case of cyclic groups of order $p^n{q}^m$ for $p,q$ distinct primes and $n,m\in \mathbb{N}$.