Yea.. no such thing as a "corner of the map" in minecraft PC.
There's several ways to mine, some are more effective than others.
What I've seen most often is to tunnel in near bedrock, then tunnel every other block between 2 shafts, that way you get maximum coverage.
There's also the method I use which proves to be almost entirely ineffective.
which would be a 2x2 tunnel in random directions near lava.
Dunno the xbox limitations, but for pc we have nearly unlimited world size, and 256 height. The ground is ~64.