The QR would be of a URL. The QR should be big enough like 4 A4 size papers. I though of cutting out the white boxes from a printed paper and spray on it but what about white dot islands. The precision needs to be good enough for a cell phone camera to detect it on the floor from standing distance.
One approach to avoid the "island" problem could be to split the pattern into two stencils. In each stencil only the holes of every other row are cut out.
First colour is applied to one of the stencils. Then the stencil is exchanged and the colour is applied to the other stencil.
The weak point of this approach is that both stencil need to be placed at the same position.
Instead of spraypaint - consider a "pavement sticker" or "footpath decal" that looks something like these.
A brighter background colour will help it stand out much more than paint on a dingy pavement/sidewalk. And you can peel, stick, stomp and go, whereas paint takes at least a minute to be touch dry, risking people standing in your tag.
Paper won't last very long, which might be suitable for your needs. A solid vinyl sticker could last up to years.
How about buying some grid-shaped welded wire metal mesh (commonly used for rabbit or chicken hutches), and using sticky tape to cover the squares you want to mask?
The wires would be thin enough that they wouldn't affect the scan, but strong enough to support isolated islands (much stronger than relying on tiny thin pieces of paper or card, which might break once they've been soaked in paint). More importantly, it would be quicker to make than a hand-cut stencil and you wouldn't need any expensive machines like a CNC router or 3D printer.
I recommend buying a flat sheet, the stuff that comes on a roll is usually twisted and won't lie flat.
Your islands can become insignificant by creating stencil like bridges to the more solidly founded segments. A bridge of a few millimeters will bleed paint underneath but also will be small enough to be ignored by the QR software from a distance appropriate to the size of the code print. If the few millimeters is excessive, hot glue applied to ordinary sewing thread in more locations (spider web?) will provide the support and almost assure bleed under.