The engine is built for high-octane gas. It performs best on 89 octane or higher. It can run on lower octane fuel, but the engine computer has to retard the timing to prevent knocking, which results in lower fuel economy. Generally, between high- and low-octane fuels, the loss of economy is greater than the difference in the cost of the fuel.
Usually BMWs have the octane requirement on the inside of the fuel door, but I haven't looked at my Z3 to verify.