I frequently use 20 or even 30 lb for bite tippet on 12 – 15 lb leader when snook/baby tarpon fishing. A double or triple surgeons knot has always been sufficient, and it is easy and quick to tie.
When going a little larger, say 20 lb tippet to 50 lb bite tippet, I use an improved blood knot – simply double the smaller tippet and tie the usual blood knot – about 4-5 wraps for the smaller doubled tippet and 2-3 wraps for the bigger stuff. Be sure to moisten the knot when drawing tight. This is Flip Pallet’s recommended knot for tarpon – if its good enough for him, it will work for me.