We know there are 18+ quintillions planets - more precisely, 264 planets.
We know 64-bit number can have 18+ quintillions values, and each can be a seed for a different planet.
We know every long integer (64-bit) number representing each of those 18+ quintillions unique values - is 8 bytes long (1 byte = 8 bit).
So, how many GIGABYTES (Gb) of data would we need to store 18+ quintillions of those numbers (planet "seeds")? Easy math:
8 x 264 bytes = 8 x 18,446,744,073,709,551,616 / 1,073,741,824 gigabytes = 137,438,953,472 Gb.
This roughly is an equivalent of ONE HUNDRED AND THIRTY SEVEN MILLIONS HARD DISK DRIVES required to store 64-bit seeds for each NMS planet ONLY, each one being 1Tb (1 terabyte = ~1000 Gb) capacity.
Modern 3.5 inch hard disk drives of 1Tb capacity are 19mm of height. So, if you take modern 1Tb HDDs, fill them all with just a SEED of each NMS planet, and put those HDDs on top of each other - then the pile of HDDs would be 137,438,953 * 19mm = 2,611,340,107 mm ~= 2611 km high.