If everything were done using 64 bit integers, the minimum distance could be decreased dramatically!
Assuming everything is signed, 32bit integers can represent up to 2^31. At 10,000km spacing, that gives us a max distance from the center of the coordinate system (presumably the primary) of 2.3 lightyears. It's probably reasonable to want to be able to go at least a lightyear, so no less than 5000 km spacing is appropriate.
With 64bit signed integers, if we want to go 1 lightyear out, we can use a spacing of about 1mm.
Using 64bit integers, a game could theoretically track the exact impact position of every weapon battery based on the direction they were fired and the position of the weapon on the ship. Though, honestly, I might go with floats anyway since my expectation is that computers have more FPUs than integer units and so it would possibly be faster. And 64 bit floats have plenty of precision at reasonable distances. But I haven't tested it in detail.