I'm not a MaxNet customer and I don't use RapidShare, but based on traceroutes I would guess that Level3 or Global Crossing would be optimal. Only way to be sure is to test each one of course.
Cogent is cheap and nasty (cheapest Tier 1 provider out there) but they have a good size network footprint, they are however prone to congestion*. Level 3 is (supposedly) a premium tier 1 provider, I've had good and bad* routing from them in the past to NZ (used to use them for my main server in US). Global Crossing have a good tier 1 connection to NZ, however you may find yourself getting routed through Asia* for Rapidshare. Other three networks are not big providers over this way. I'd go with Level 3 or Global Crossing (try them both).
*My opinions based on previous test results over the last ten years
If anyone else is interested in this, I've run some tests and received the following results. My connection was around 4.8MB/s to Auckland on Speedtest.net during the testing.
Using a download manager which downloads 10 sections of the file at the same time.
Deutsche Telekom (11 Hops, through America)
1) s485dt.rapidshare.com - 470KB/s
Cogent (18 Hops, through America)
1) rs485cg.rapidshare.com - 460KB/s
As Ilmarin/kingjj said Global Crossing gave the best result, however it also gave one of the lowest, so I think in a lot of cases it just depends on your luck of the draw as to what Rapidshare server you get connected to.
Not surprising, really. I've switched between different upstream providers when downloading from Easynews in the past, and seldom noticed much difference, but certain providers do occasionally have a bad day (e.g. if they have unresolved network faults), so I think that's the primary value of being able to select your route.
I think you'll find that all those routes go through America (some via Australia first), but you mistook the asianetcom.net hops as being via Asia when they are actually NZ to US direct.
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