Beware open vias near pads
Having open vias in pads is just about the number one "do not do" when creating a printed circuit board. Number two or three is don't have open vias near pads without a solder mask dam to stop the flow of solder.
Don't do this:
Here's what happens:
Your assembled board will likely have open connections between some of the BGA balls and the board.
If you are putting the via IN the BGA pad, as you would need to with a fine pitch BGA, your only choice is to have the vias filled and plated over at the board fab house. (Read this post). If you're putting the vias between the pads, you have two options. You can put soldermask dams on the short trace between the pad and the open via. This will prevent solder paste from migrating. I've modded the image below to show what that would look like.
The other, and better, option is to completely cap the vias with solder mask. This gives a bit of extra protection in case any of the solder mask dams are too thin or chip off. Just make sure you cap these things on the solder side. If you cap them on the back, solder can still spread on the trace and partway into the via. That would still put the electrical and mechanical connection at risk.
Solder shall not pass off the pad.
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