satisfies all of these constraints (i.e. no phonon scattering, no weak localization, temperature much lower than the fermi temperature) very well.

Although the [*mobility*]{} enhancement of 2D systems has generally led to the improvement of sample [*quality*]{} on the average over the years as manifested in the observation of new phenomena, it has been known from the early days that the connection between [*mobility*]{} and [*quality*]{} is at best a statistically averaged statement over many samples and is not unique, i.e., a sample with higher mobility than another sample may not necessarily have a higher quality with respect to some specific property (e.g., the existence or not of a particularly fragile fractional quantum Hall plateau). Thus, higher (lower) mobility does not necessarily always translate into higher (lower) quality for specific electronic properties. Since 2D carrier mobility is a function of carrier density [@dassarmaprb2013], in fact, it is, in principle, possible for a sample to have a higher (lower) mobility than another sample at higher (lower) carrier density, implying that the measured mobility at some fixed high density is not (always) even a good indicator of transport quality itself as a function of carrier density, let alone being an indicator for 