the text coded invoice is actually smaller than the QR code
The QR code isn't necessarily shown in the smallest size it can be while still being recognizable. I'd guess it's the opposite: it's shown the largest it can be.
The QR code involves an error correcting code (Reed-Solomon) which can eat about half the area (depends on the settings with which the code was produced). So double your text area to accomodate the error correcting codes.
Once you do that, I believe that the QR code would actually win in efficiency in terms of size. That doesn't mean that you can't use letters if you want the thing to be human-readable, but for invoices it would be a whole lot of letters.
yeah this. Depending on your chosen error correction, you could have a year-old smudged and ripped QR code still scan. If you smudge even a single letter of text, forget about it.
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OK, but is this really an advantage for this use case? Here the invoice is displayed on a screen and there is no way for it to degrade in that way.
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also there are letters and numbers that are visually ambiguous (1/l, 0/O, etc). In binary and with error correction it's easy.
QR can also be animated, allowing for a huge amount of data.
wish I could find a cool article I read a year or so back, but the wikipedia page is pretty interesting too:
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