This is an interesting read, it is dated before the twin scroll turbo days, so it is unclear if the advice still applies to N20/N26 in F30:
"Thomas Plucinsky, BMW Product and Technology Communications Manager told us all BMW engines are designed to run on 91 octane. All performance testing, including EPA emissions and fuel mileage, is done with 91 octane. However, though BMW is all about performance, their motors will run on 89 or 87 octane without damage. The knock sensors pull the ignition timing back and eliminate detonation. There will be a loss of power and a decrease in fuel mileage, but the size of the horsepower loss and the increase in fuel consumption depends upon many factors, such as ambient temperature, exact formulation of the fuel and driving technique, so BMW does not offer any estimates for operation on lower grade fuels. One not so obvious concern, Mr. Plucinsky noted, is the type and quality of additives the gasoline companies include in the fuel. Premium gasolines may have better additive packages which are more effective keeping fuel systems (particularly injectors) clean and working efficiently, than those in regular grade fuels or off-brand products. Using lower octane or off-brand fuel could be degrading the fuel system over time, setting you up for a repair bill down the line."
The last point of the quote is to use gasoline with good additive packages, but implies premium gasoline has better additive packages than regular gasoline, however top tier retailers(e.g. Costco) advertise all their grades carry the same additive packages.