The 222 Rimmed would be ideal, but it is not seen over here in the UK or in Europe - it was an Australian innovation. Heaven knows how I would get brass etc. The 218 Bee, doesn't have much more than the 22 Hornet and doesn't push a 50gn bullet fast enough to meet the 1,000 ft/lbs of muzzle energy requirement.

The 5.6x50R is another step up in terms of power and pressure from the .222.

I suppose you could always make in .222, and then figure out having some sort of spring loaded extractor for a rimless cartridge.