I don't know the answer to your question, but don't go for the cheap ones - get the ones with multiple lugs. They are the ones that stay in place once fitted.
I have bought cheap ones of Ebay. They do the job.
My originals corroded away and have seen similar corrosion on cars just over a year old.
My Ebay set are now a year old and are perfect.
The set I had on my previous wheels 2 years old also perfect when I sold them.
The originals are overpriced for something that's going to look nasty so soon.
I just bought a set for £8.89 and they look fine I You can tell they aren't originals up close ie. when I had them in my hand for fitting them but now they are on the car they could easily pass for genuine BMW ones
I bought a set of e bay and they are identical to the original ones fitted, same amount of lugs for gripping and same marking on the inside . There are a lot to choose from on E bay look for the ones with the same lug spacing as originals. these seem to be fine
When putting new centre caps on put Vaseline/Grease or similar all over the back to prevent water ingress works wonders for the OEM Badges and prevents the issues described above
Seen this on Jaguars.
Why something that draws the eye that shows the brand, then corrodes in twelve months, just because they think they will save a few £ ( there's no Euro symbol on my keyboard? ) is false economy.
Have seen worse though, the centre badge on an aircraft control wheel that as melted and dripped down like candle wax, talk of cheap!
You can buy actual caps, I think BMW originals can be had on eBay for £15 but make sure to buy the newer kind not the dated type with both chrome and plastic surround. Alternatively you can get 68-70mm metal domed stickers.
The stickers actually look better than the caps because they have no chrome surround and cover up the existing BMW chrome border, even better for black alloys. Just make sure to apply it carefully because once stuck you can't get it off without damaging it.