some party was able to bribe the lab that conducted the exam and put remote access software into the computer
This is the core of your problem. When someone has physical access or control of device, it is difficult to prevent them from doing unintended things with it.
You don't give much detail on the lab or the testing process, however...
Is it possible to block some port from lab local router? Or it is possible to blacklist all traffic except the examiner server connection? In one lab there are 200 or 250 computers. Or is there a way to stop those remote access software or prevent installation?
...you go on to ask these questions which makes it seem that it is only individual staff at the site that is the problem, but the "lab" itself may be operated/controlled by the government.
If you control the network, you certainly can limit or deny access to or from the lab computers. This just takes proper consideration and planning. Keep in mind that there are many ways to circumvent restrictions, so it is best to give minimum access only to essential resources.
As for preventing installation of software, that would depend on the operating system, but most operating systems have multiple means of limiting user access. Permissions, user rights, and/or policies can be implemented to help prevent things like software installation or access to portable media (i.e. USB flash drives, etc).
Outside the operating system, I have seen products such as Deep Freeze used to great effect in university computer labs for similar reasons. Any changes following the point at which the computer image is frozen will be removed following a simple reboot. It is often common practice in such teaching labs that the computers must be completely powered down before a test to remove any changes.
I have also seen several different classroom monitoring applications that allow an instructor (or third party outside the classroom) the ability to monitor what is taking place on computers in a lab from a central computer/location. This may be as simple as viewing what is taking place on the screens to things like reports on application in use (both in foreground and background).
There are many options out there, which ones and exactly how to implement would require knowledge of your environment, knowledge of your needs, and how many resources you have available (i.e. money, staff, etc).