"This means a mine's radius of action is at least half a cube side, or 150 million miles (in this example, anyway)."
Given that the mines are 10 KILOTONS in size..that's not entirely unreasonable.
Of course its all quite abstracted. I can imagine a SE623622565616 where everything is simulated in total detail.
I can also imagine that requring more computer power than exists on the planet today to compete the movement of one ship.