Your 100mg nic will need to be diluted to 16% of the final mixture to achieve 16mg concentration:
16% nic base (PG)
Being only 1.6% of the final mixture, the nic content can pretty much be ignored from here on out, and so you
basically have 16% PG in the mix at this point. Since you want a final concentration of 65%, you need to add another 49% pure PG:
16% nic base (PG)
49% PG
Now, you just need to add the remaining 35% VG and you're all set. Add them all up, and you have:
16% nic base (PG)
49% PG
35% VG
---------------------
TOTAL: 100%
Now, just take these %'s and multiply them by the desired amount of
e-liquid. For example, if you wish to make a 30ml bottle, you would have:
30ml * 16% =
4.8ml nic base
30ml * 49% =
14.7ml PG
30ml * 35% =
10.5ml VG
-------------------------------------
TOTAL: 30ml
EDIT: Technically, this will give you a mixture of 1.6% nicotine, 63.4% PG and 35% VG since the nic base is not 100% PG but rather only
mostly PG with a little bit of nicotine in it, also. If you
really want to account for the nicotine, and have the
remainder of the liquid be a straight 65/35 mix, then you're looking at:
1.6% pure nicotine
98.4% "other"
Of that 98.4%, you want 65% PG and 35% VG:
65% * 98.4% =
63.96% PG
35% * 98.4% =
34.44% VG
----------------------------------------
TOTAL: 98.4%
So in the end you're looking at:
1.6% pure nicotine
63.96% PG
34.44% VG
----------------
TOTAL: 100%
Now note that the PG in the nicotine solution will account for 14.4% of that PG. So the final mix would be:
16% nic base
49.56% PG
34.44% VG
-----------------
TOTAL: 100%
This breaks down as follows:
1.6% pure nicotine
14.4% PG
from the nic base
49.56% PG (additional)
34.44% VG
-----------------
TOTAL: 100%
...but, keep in mind that numbers like 49% and 35% are a lot easier to work with than 49.56 and 34.44, and won't make that much difference (less than 1%) in the final product. When you're only working with a few mils of liquid, your margin of error is probably higher than that anyway, making this kind of precision unnecessary. We're talking 14.868ml of PG (in a 30ml mix) instead of 14.7, and 10.332ml of VG instead of 10.5. The difference is less than .2ml in either case; less than 1% of the total volume. If you think you can accurately measure 14.868ml of PG, then by all means go for it, but if you decide to just say "ah, fudge it" and use 14.7ml instead, I doubt anyone will know the difference.