\begin{table*}[ht]
\centering
\caption{Fisher $1\sigma$ uncertainties on $H_0$ from GW memory. The column $N=100$ gives the constraint from exactly 100 detections within $d_{L,\mathrm{near}}$ (the volume used for Bayesian sampling), computed by Fisher scaling: $\sigma(N_{100}) = \sigma_{N_\mathrm{det}}\sqrt{N_\mathrm{det}/100}$. $N_\mathrm{lo}$ and $N_\mathrm{hi}$ are the expected total detections over the full detectable volume at the low and high merger rate bounds respectively. Each cell shows mean\,$\pm$\,population scatter\,($\sigma_\mathrm{pop}$) with Monte Carlo error in parentheses.}
\label{tab:sigma_H0_combined}
\begin{tabular}{lrrrrccc}
\toprule
\multirow{2}{*}{Detector} & \multirow{2}{*}{$T_\mathrm{obs}$} & \multirow{2}{*}{$f_\mathrm{min}$} & \multirow{2}{*}{$M_\mathrm{max}$} & \multirow{2}{*}{Approx.} & \multicolumn{3}{c}{$\sigma_{H_0}$ [km\,s$^{-1}$\,Mpc$^{-1}$]} \\
\cmidrule(lr){6-8}
 & [yr] & [Hz] & [$M_\odot$] &  & $N=100$ & $N_\mathrm{lo}$ & $N_\mathrm{hi}$ \\
\midrule
\multicolumn{8}{l}{\textit{aLIGO/Virgo}} \\
 & 8 & 5 & 100 & MWM & -- & 12.9 $\pm$ 5.0 (1.6) & 7.88 $\pm$ 3.05 (0.96) \\
 & 4 & 5 & 100 & MWM & -- & 12.9 $\pm$ 5.0 (1.6) & 7.88 $\pm$ 3.05 (0.96) \\
 & 16 & 5 & 100 & MWM & -- & 12.8 $\pm$ 5.1 (1.6) & 7.82 $\pm$ 3.09 (0.98) \\
 & 8 & 20 & 100 & MWM & -- & 12.9 $\pm$ 5.0 (1.6) & 7.90 $\pm$ 3.06 (0.97) \\
 & 8 & 40 & 100 & MWM & -- & 15.9 $\pm$ 10.6 (3.3) & 9.71 $\pm$ 6.48 (2.05) \\
 & 8 & 60 & 100 & MWM & -- & 13.5 $\pm$ 4.6 (1.5) & 8.25 $\pm$ 2.83 (0.90) \\
 & 8 & 5 & 80 & MWM & -- & 12.2 $\pm$ 3.4 (1.1) & 7.47 $\pm$ 2.06 (0.65) \\
 & 8 & 5 & 100 & MWM$^\dagger$ & -- & 11.8 $\pm$ 4.8 (1.5) & 7.21 $\pm$ 2.94 (0.93) \\
\midrule
\multicolumn{8}{l}{\textit{ET}} \\
 & 8 & 2 & 100 & MWM & -- & 1.04 $\pm$ 1.19 (0.38) & 0.601 $\pm$ 0.686 (0.217) \\
 & 4 & 2 & 100 & MWM & -- & 1.02 $\pm$ 1.21 (0.38) & 0.586 $\pm$ 0.696 (0.220) \\
 & 16 & 2 & 100 & MWM & -- & 1.16 $\pm$ 1.19 (0.38) & 0.668 $\pm$ 0.688 (0.218) \\
 & 8 & 5 & 100 & MWM & -- & 1.06 $\pm$ 1.21 (0.38) & 0.611 $\pm$ 0.698 (0.221) \\
 & 8 & 20 & 100 & MWM & -- & 1.00 $\pm$ 0.62 (0.20) & 0.579 $\pm$ 0.360 (0.114) \\
 & 8 & 40 & 100 & MWM & -- & 0.718 $\pm$ 0.366 (0.116) & 0.415 $\pm$ 0.211 (0.067) \\
 & 8 & 2 & 80 & MWM & -- & 0.777 $\pm$ 0.679 (0.215) & 0.449 $\pm$ 0.392 (0.124) \\
 & 8 & 2 & 100 & MWM$^\dagger$ & -- & 1.14 $\pm$ 1.14 (0.36) & 0.656 $\pm$ 0.657 (0.208) \\
\midrule
\multicolumn{8}{l}{\textit{CE}} \\
 & 8 & 2 & 100 & MWM & -- & 0.626 $\pm$ 0.508 (0.161) & 0.362 $\pm$ 0.293 (0.093) \\
 & 4 & 2 & 100 & MWM & -- & 0.619 $\pm$ 0.515 (0.163) & 0.357 $\pm$ 0.297 (0.094) \\
 & 16 & 2 & 100 & MWM & -- & 0.624 $\pm$ 0.505 (0.160) & 0.360 $\pm$ 0.291 (0.092) \\
 & 8 & 5 & 100 & MWM & -- & 0.626 $\pm$ 0.508 (0.161) & 0.362 $\pm$ 0.293 (0.093) \\
 & 8 & 20 & 100 & MWM & -- & 0.565 $\pm$ 0.471 (0.149) & 0.326 $\pm$ 0.272 (0.086) \\
 & 8 & 40 & 100 & MWM & -- & 0.625 $\pm$ 0.498 (0.157) & 0.361 $\pm$ 0.287 (0.091) \\
 & 8 & 2 & 80 & MWM & -- & 0.679 $\pm$ 0.550 (0.174) & 0.392 $\pm$ 0.317 (0.100) \\
 & 8 & 2 & 100 & MWM$^\dagger$ & -- & 0.526 $\pm$ 0.429 (0.136) & 0.304 $\pm$ 0.248 (0.078) \\
\bottomrule
\multicolumn{8}{l}{\footnotesize $^\dagger$ MWM waveform with NRSur7dq2 prior bounds ($q\geq0.5$, $|\chi|\leq0.8$).}
\end{tabular}
\end{table*}