Let's assume the caster of Tenser's Floating Disk has a speed of 6000ft (for no particular reason), that is more precisely, they can cover 6000ft in 6 seconds.
However there are limitations on the disc's movement:
If you move more than 20 feet away from it, the disk follows you so that it remains within 20 feet of you.
and
If you move more than 100 feet from the disk (typically because it can’t move around an obstacle to follow you), the spell ends.
as well as
It can move across uneven terrain, up or down stairs, slopes and the like, but it can’t cross an elevation change of 10 feet or more.
Does the spell text of Tenser's Floating Disk, or other rules tell us enough, to say when the disk's movement/following happens? Instantly? At the end of turns? End of movement chunks?
Say that if the caster moved 200ft east as one part of their movement, then separately moved 250 ft west, the spell ends part way through the first part of the movement, even though you end up less than 100 ft away from the disk? If the spell doesn't end part way through the movement, does it attempt to travel east first then west, or just 50ft west.
Can the caster make the journey in 95 ft bursts, so as to not risk ending the spell early, letting the disk catch up each time?
Can the caster complete a 5900ft maze in a single movement, and end up ~100ft from the disk, and if so what path if any does it take?
Can the caster run round an obstacle course with disk following it like a prize dog, so long as it's not forced to traverse inclines of more than 10ft? Does it skirt around such obstacles (hypothetically losing points) or does it attempt a 12ft high bridge (with slopes either side) even though it would be crossing over an elevation change of more than 10 ft thus ending the spell, or does it 'lazily' go around? Does it matter if the disk is teased up in 9ft increments? We know it can 'take corners', but is that it? We know it likely can't do 'path finding': Can magical constructs pathfind?
In short, how closely can the disk follow the caster's path based on when it starts to follow the caster, vs. just staying within 20ft?
Best Answer
The disk follows you as you move.
When the caster is 21 feet east of the disk, the disk moves one foot east. That's what "the disk follows you so that it remains within 20 feet of you" means. So in the circumstance you describe (moving 200 feet east then 250 feet west), there's no point during that movement where the disk isn't within 20 feet of you. The disk doesn't have its own turns or take actions; it just follows you as you move.
As for other details of how the disk moves, it's up to the DM. As long as it is (a) trying to stay within 20' of the caster, (b) no more than 100' from the caster, and (c) not traversing obstacles it can't pass, it could be as smart or dopey as the DM chooses. Maybe the disk has personality and acts like a loyal dog. Or a truculent mule. Maybe it just optimally implements the A-star route-finding algorithm and does so using spatial information not available to the spellcaster.