The TrustedReviews.com ISO test scene in full.
This 100% crop taken at ISO 160 shows no trace of noise.
Likewise, ISO 200 is also pin-sharp and noise free.
At ISO 400 there is just a hint of softening, but it's only visible at 100% and above.
At ISO 800 and the GF3 is still keeping noise to an minimum.
By ISO 1600 noise is becoming more visible as the image begins to soften, but only at higher magnifications. At more regular sizes images shot at this sensitivity still remain very usable.
By ISO 3200 you are going to see the effects of noise whatever size you view the image
ISO 6400 is really only for use in emergencies.
The GF3 does especially well at medium-fast sensitivities like ISO 800, where regular compacts tend to suffer
ISO 1600 - 100% crop
ISO 3200 - 100% crop
IS0 6400 - 100% crop