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Currently EFI partitions are on the order of 300-500 MB for common installs, that'd allow you to store millions of PNG-compressed QR codes.

Or even better, a small library which'd allow bootloader to generate it on the fly.

On my system the full qrencode binary is 85K, and it supports a lot more output formats than needed in this application.

http://fukuchi.org/works/qrencode/index.html.en

That said, with iPhone cameras supporting live OCR and URL detection, a QR code would be unnecessary.

You don't need to store the whole QR code, just code to convert an URL into a QR code. Or a good, short URL that can easily be typed, e.g. "microsoft.com/errors/1234"

A 50 character capacity QR code requires a whopping 137 bytes to store as a raw image.