I have long been conflicted about the whole Eugenics thing. It does make a certain sort of intellectual sense - in any society there will be a percentage of the population who contributes nothing. They leech the resources of social programs intended to help people who need short term assistance. They commit crimes and are a stain on society. Why not get rid of these people?
The biggest problem, I think, is that a person's value is derived from far more than their score on an intelligence test.
Take myself, for example. I would be worried if such a mandate were passed where I live. If they set the bar high enough, I would be required to kill myself. But I am an outstanding citizen. I'm a veteran, active in my community; I'm a husband and a father. I contribute value to my community.
How would I match up against a genius; a truly remarkably brilliant man, but one who has murdered twenty seven women and used their skin as upholstery? Or what about a woman who drowned her children, but who also had a doctorate in medicine and healed thousands of people?
Who is more valuable to society; a man of moral character who eschewed higher education in favor of service in law enforcement or a woman who's research has led to sustainable energy, but who kidnaps children that remind her of her deceased baby?
If there are going to be exterminations going on, it should at least be done on an individual basis.