[RedDevil]

Speedometers are designed to slightly overstate the speed.
Over here the indicated speed is legal if it is no more than 10% over the real speed - and no less than 0% under.

That's right - a speedo that indicates 0.00001% less than the actual speed would be both insanely accurate and illegal.
So, generally speedos are about 3% optimistic - or slightly more, as it helps sales if the car appears silent, comfortable and powerful at the indicated speed, while it is in fact going slower than what you'd expect.

Odometers OTOH need to be correct; both overindicating and underinicating are unwanted, as the first would throw the car out of warranty quicker and the latter would assume less than actual wear on the car if you sell it.
So the car will show distance quite correctly on OEM tires.

If you get taller tires than OEM you probably get a small economy boost, but it won't show as the bigger tires mean you see less miles on the odo for the same distance.
Likewise, undersize tires will make your economy by the meter look good - but your real mileage would be lower than indicated.

Oversized tires on 13" rims would need to have giant sidewalls. They would be hard to get. Better settle for top tier tires in a more common size.
IMHO top quality tires live longer, make less noise and have more grip than the cheap or odd ones.