Is a 40 amp sub panel permissible
What is the smallest allowable sub panel in amps?

Yes, it is permissible. I don't think there is a "limit," on how low you can go, but the size subpanel you run generally depends on the loads you are hoping to use. You might want to list specifics such as:
-length of the planned subpanel from your main panel and where it is going.
-types of things you plan on running from this subpanel (lights, furnace, tools, receptacles etc.)

You can feed a secondary panel board with just about any amperage you want. Main Service Panel Board must conform to the POCO offered standard amperage ranges.

Right now here in Virginia the minimum allowed for a residence is 100 Amps and 120/240 Volts.

Basically for a secondary panel board, you need to know whether the board will be in the same building as the main service panel board or in a remote building.