So if you are confused by the documentation of that attributes, yet it doesn't work, that's why.
See the W3 page for the versions.
I find it easiest to use Javascript, s the other answers say, since you can just use a pre-made module. Also, many Javascript date picker libraries have a min/max setting and have that nice calendar look.
I've intentionally added the max attribute with a date far into the future, because it seems Chrome browser change the width of the field once a max attribute is set, so to avoid that, I had it pre-set.