There typically isn't a minimum size. Most (if not all) airlines have a max bag size and weight, and if the bag exceeds that, they add a fee. For example, FL
allows a bag up to 62 inches (length+width+height). Any bag that is 63"-80" has an additional $65 charge per bag and anything over 80" is not accepted (with some sporting equipement exempted [like skis]). DL
has a similar policy, but charge $100 per bag for any bag between 63"-80".