It's possible to get around 32-bit effective resolution with an LTc (Low critical temperature) DC SQUID (Superconducting Quantum Interference Device) using well-executed hybrid digital/analog techniques. A few \$\mu\Phi_0\$ RMS noise and, say, +/-10000 \$\Phi_0\$ range gives 32 bits with 1Hz bandwidth and 0.3Hz corner frequency. Actual critical current is at least an order of magnitude higher so a few more bits might be possible.
Good for making picovoltmeters and such like. Kind of expensive and inconvenient because of the 4K environment.