You can create floating carpets by placing them repeatedly in liquids. I don't think it is a client-server desync, because they stay when reloading the world.
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ampolive
Arisa Bot
Thank you for your report!
We're tracking this issue in MC-17833, so this ticket is being resolved and linked as a duplicate.
That ticket has already been resolved as working as intended, which means this is not considered a bug and won't be fixed. Please do not leave a comment on the linked ticket.
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Duplicates MC-17833. Of course I find it after I create the issue.