The uncertainty of the location would grow with the number of sampling points, given constant time distance. In this case, many data points could yield the momentum with greater (statistical) accuracy, but the time resp. location will lose its accuracy.
F.e., with 1000 samples the momentum could be calculated with a certain better accuracy. But the location resp. the time, when this momentum is valid, is smeared over the path of this particle within 1 microsecond. The changes in the momentum for a few nanoseconds are smoothed out to an average value valid for the total interval of 1 microsecond.
Heisenberg did not only derive the momentum-location uncertainty, but also the uncertainty for time-energy resp. time-frequency, since E=hf.
One and only 1 sample point in the time domain is equivalent to a Dirac impulse functional.
It has the maximal accuracy in time, since it defines one single time point.
But in the frequency domain, this sample results in a constant, i.e. all frequencies are equally contained in this sample yielding maximal uncertainty.
In mathematical words: The Fourier or Laplace transform of a Dirac functional yields a constant - and vice versa, i.e a constant in the time domain yields a Dirac functional in the frequency domain.
If the number of sampling points in the time domain is increased, the uncertainty in the frequency domain would be decreased. Obviously the uncertainty in the time domain would be increased, the frequency/energy information would be no more able to be mapped to a single time point.
Caveat: The time point of a sample is - in theory, not in reality - smaller then the Planck time.