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RAID6 with 2 drives per machine
With RAID6 you can lose two disks and keep your data, but of course the CPU required is greater. That would mean you could run mini-ATX boxes with big disks and still have some chance of keeping your data intact.
You could probably do this with some of the NAS drive cases that I've seen, although it would be easier if you could load the netblock system onto each drive, but since mostly then run linux it might be possible. We may even see it as a standard option...
I think a purpose-designed system will work better than trying to run RAID over the network though - in theory you should be able to satisfy any RAID5 request by sending full data from N-1 drives and a checksum from the last one (at a computational price on the requesting drive) which would lower your newtwork demands.