The basic strength of alkylamines does not depend on which of the following?

Presence of an aromatic ring

Since only basicity of alkylamines is in question the presence of aromatic ring is not considered. As the size and number of alkyl groups increases, the stability of ammonium ion  increases due to dispersal of more positive charge by the +I effect of alkyl groups. The physical state, gaseous or aqueous, also determines the basicity as the hydration effect comes into play.