I checked this https://unicode-org.github.io/emoji/emoji/charts-15.0/emoji-list.html and it seems updated to unicode v15.1. Where do you count 3664?
Btw, some emojis have just a slight difference, e.g. color, and this could make harder recall the correct one.
1. Skin color, gender etc nearly double those 1874 in the unicode list
2. It's ok if you don't recall the correct one exactly, because you have infinite tries and know what to look for
There is only 1874 base emojis? That's too few. If you cut to 1024 from that, it's 10 bits per symbol and you'd need to extend to 14 for the same bit size.
I think 2048 symbols is too many, also.
But so long as you give the set as an input panel, ok.
