Since the 1950s, it has been conjectured that quantum fluctuations of the spacetime metric might make the familiar notion of distance inapplicable below the Planck length.[23][37][22] This is sometimes expressed by saying that "spacetime becomes a foam at the Planck scale".[38] It is possible that the Planck length is the shortest physically measurable distance, since any attempt to investigate the possible existence of shorter distances, by performing higher-energy collisions, would result in black hole production.

https://en.wikipedia.org/wiki/Planck_units#Planck_length

Same is true for the Planck time, although the English Wikipedia is oddly blank for that one: there can be no space or time smaller than that within the physics that we have come up with.