Sorry to say that, but renting a good apartment is a rocky road. There's plenty of gotcha's to watch out for. Look at the forum - at least you don't have toddlers above, neighbours working on night shifts, people with certain affinity towards noise and parties, etc. You could have done some basic reconnaissance before renting the place - asked the neighbours (there might be people for whom the noise is acceptable but who are aware of it). If the noise is within the legal bounds then it would be good to find out what is the source of the noise and then. It might just need some fine-tuning or maintenance - talk with consierge, etc.
PS. If it's monotonous humming then ear-plugs should be perfect. Some would like such sound as it tends to mask other more artificial ones. However this is a very individual issue...
It turned out that there are ventilation pipes exiting on the roof and we are on the top floor -- amazignly, other neighbours do not have that problem because for some reason the stinking discharge lingers on the roof.
We should have done a better research -- there is a restaurant on the ground floor, so now at least we know that we would never rent a flat where there is a restaurant near.
We complained to the property management company several times. Other neighbours from the top floor did the same. The owner annulled the lease agreement with the restaurant, the restaurant appealed to the tribunal, I was summonned as a witness -- two years later the restaurant is still there but the situation improved -- I guess the owner was required to make some modifications in the ventilation and sewage system.
Check with the concierge if the noise remains and can not be switched off -- perhaps it is not normal and maybe the owner can do something about it.
It just took a call to the heating engineer (via the landlord) who came over and found that the revolutions of the pump were too high. He dropped them and the noise went away.
Sometimes a really simple problem can cause such a big headache!