Octane number indicates how much can you compress the air and fuel mixture without causing it ignite spontaneously. Higher octane number means you can apply higher compression. Increased compression ratio means that the same amount of air + fuel mixture will generate more force for every revolution of the engine. So to generate more power luxury cars use high compression ratio engines that requires higher octane number fuel to resist the spontaneous ignition before actual ignition by the spark plug. Some cars also use direct gasoline injection to avoid spontaneous ignition.
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