Just tested this on a couple of maps, doing one lap of the outer road nearest the beach. It will of course vary depending on which world you are in.
World 12 (the star shaped world) gained me 216 792. This might be one of the shorter roads due to its fairly regular shape.
World 2 (more of an odd shape) gained me 286 643, itโs one of the weirder shapes so that might put it near the top of the range.
So the number 250 000 quoted on @Anticosmic 's blog seems a fair average for one lap.
Explorer is granted for 1 000 000 (so this would be 4 to 5 laps of the outer road).
Cartographer is granted for 4 000 000 (= somewhere between 14 to 18 laps depending on which world).
Muledump will give you a guaranteed correct count of your travels. **Remember youโll need to nexus after every lap to clear the minimap - because it only counts as explored when it changes from blackspace to uncovered on your minimap.**