= Solution
A survey depth $R\sim400\,\mathrm{Mpc}$ makes wavelengths substantially larger than its volume poorly measurable. A characteristic inverse depth is $1/R\simeq2.5\times10^{-3}\,\mathrm{Mpc^{-1}}$; a Fourier wavelength that fits across a dimension $L$ instead requires $k\gtrsim2\pi/L$. For $L$ between $R$ and $2R$, this is roughly $0.008$--$0.016\,\mathrm{Mpc^{-1}}$. A limited sky patch can have smaller transverse dimensions, so its <survey window function> raises the practical minimum in those directions. An indicative useful band for a broad survey is \b[around $10^{-2}\,\mathrm{Mpc^{-1}}$ and above], including scales near equality if its volume is large enough.
There is no upper <wavenumber> determined by depth alone. Mean separation of observed galaxies, <galaxy power spectrum shot noise>, angular/redshift resolution, and nonlinear clustering set it. Straightforward linear inference is typically restricted to roughly $k\lesssim0.1\,\mathrm{Mpc^{-1}}$ at low redshift, with smaller scales requiring modelling. The magnitude limit does not specify the galaxy <comoving number density>, so a more precise sampling cutoff cannot be deduced from these data.
The two measurements are complementary. The <cosmic microwave background> samples a large volume at an early epoch when relevant perturbations are mostly linear, and is free of <galaxy bias>; its matter-spectrum inference is indirect and depends on projection, cosmological parameters, foregrounds, and <cosmic variance>. A <galaxy survey> gives three-dimensional late-time information and can reach smaller scales, but observes biased, discrete tracers: <galaxy bias>, nonlinear gravitational growth, <redshift-space distortions>, selection effects, and <galaxy power spectrum shot noise> must be controlled. Combining both constrains the initial spectrum and its subsequent growth more strongly than either alone, while their overlapping modes test the inferred evolution.
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