Bigger tires do not lead to better gas mileage, because they weigh more than smaller tires. Smaller tires that weigh less provide better fuel efficiency.
Bigger tires also typically require larger or wider wheels, which add additional weight and reduce fuel efficiency. Research has also shown that fuel efficiency increases for a tire as the tread wears down and the treads become more shallow, because the tire weighs less. Tires that are made specifically to increase fuel efficiency are designed with shallow treads to eliminate as much weight as possible. Regardless of the size of a tire, it is important to properly inflate it to maximize fuel efficiency. Tires that are flat or under-inflated reduce gas mileage.