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My barrel is 1/7.5 and that stabilizes the 115s no problem. I'm not sure what the minimum twist is for 105/108 but i would think that 1/8 would be just fine.
It the US many shooter only need 1-7.8" to stabilize some 115gr bullets but you can get a nasty surprise so Berger recommends 1-7" for its 115gr VLD.
The 108gr Berger BT is very similar to Sierra's 107gr SMK so 1-8" is good.
You can find some very interesting information here: http://www.appliedballisticsllc.com/Bullets.html
In particular, Hornady 105gr A-Max does not work very well with Hornady recommended 1-9" twist and Berger new 308 230gr Hybrid has a 0.912 G1 BC!