Is 11 tooth the smallest easily attainable freewheel cog?

What I am after is setting up a 1:7 gear increase on something and bike gears seem like a decent starting point. I thought about making my own sprockets, but that would take a ton of work to do the math and I don't quite have the right tooling. I could probably hack it to make something "work" but it would be pretty ugly I'd think.

If an 11 tooth is the smallest then for a 1:7 I would have to have a 77 tooth chain ring. That appears to be a hard thing to come by - much over 50's seems to me more custom. Folding bikes look like they are in the low 50's (small wheel bikes - 20" or so).

Is there a limit to how small a sprocket can be for a normal bike chain? Like 5-7 tooth? I realize the limit on a normal freewheel is the diameter of the spline the cogs stack up on, but with a small shaft/bearing diameter of a different set up that wouldn't be a limitation.