In so far as ultimate precision cannot exist, neither can exact values of one metre nor exact values of one ohm.
As you imply, the definitions of both distance and resistance are in principle capable of being realised to an arbitrary level of precision.
Some matters of personal interest:
Time and distance are (currently) directly related to the same basic
physical phenomenon (currently the hyperfine levels of Cs133) at 0 Kelvin), but
Time is currently transferred between standards laboratories with ~10-15 precision. It is thought that refinement of cold-trapped ions could reduce this to ~10-17, although this would probably require that the standard be redefined.
Distance measures can only be proved to agree to ~10-11
In principle, the Ohm should be defined with respect to the physical constants of time &
distance (as defined above), and e/m. As the Josephson junction provides a suitable link, it is defined
via Josephson junctions and the quantum Hall effect; however, the repeatability is only ~10 -8 and I'm not sure whether there is significant additional discrepancy between this and the theoretical definition.
In any event, that would mean that our present theoretical construct of pi ohms (using at most 16 ideal resistors) is 'only' about an order of magnitude less precise than allowed by existing transfer standards (except of course that contact resistance and measurement noise mean that we cannot measure small resistance values to anything like this accuracy...).
