If it's a square 381km x 381km then that's 145161km² (and I'm not aware that there's any difference between "square kilometres" and "kilometres squared", is there?)
Beginning with PDF 1.6, the size of the default user space unit may be set with the UserUnit entry of the page dictionary. Acrobat 7.0 supports a maximum UserUnit value of 75,000, which gives a maximum page dimension of 15,000,000 inches (14,400 * 75,000 * 1 ⁄ 72). The minimum UserUnit value is 1.0 (the default).
15 million inches happens to be exactly 381 km Source
Remark: The side length of the square correspods to 381 km, subsequently, its area is 145161 km^2 .
381 km^2 are slightly smaller than the city of Cologne.
I think the play would be to get one that's modular (I suspect it's been done) and just keep building it out. The trick would be if the Earth is flat enough of it to sit nicely on. If not, you could cheat by slightly changing the DPI further from the center, so it would be a sphere section.
Physical size is just a parameter, unless you insert formatting and stuff which needs to save data per page/region. Otherwise you can have just vector graphics of fixed data size which gets scaled on rendering to fit the physical limit.