Posits seems to be better for 8-bit or even 6-bit. There is only one not-a-number place, the NaR (not a real). This means for 6-bit posits you have 63 points in the number space.
The way posits focus on numbers near 1.0 is probably going to have a bigger effect. A 6 bit float with 4 exponent bits is the best competitor to a 6 bit posit, and it would only have four non-finite numbers.
https://en.wikipedia.org/wiki/Unum_(number_format)#Unum_III