A boot sector virus infects the master boot record (MBR) of a hard drive, the sector that contains information required to start the operating system after the computer is turned on. This type of virus is particularly insidious because it loads into memory immediately upon booting and before most antivirus programs start. This makes it possible for the virus to evade detection and removal, and can easily reinfect a system even after the operating system is reinstalled if the boot sector is not cleaned.

Boot sector virus: Given that the malware infection returned after the OS reinstallation, it's likely that the virus was not removed from the boot sector during the reinstallation process. Reinstalling the OS without cleaning the boot sector won't remove the infection, allowing the virus to continue to affect the system.

Other options:

Trojan: A Trojan is a type of malware that disguises itself as legitimate software. While Trojans can be persistent, the reinstallation of the OS should remove any Trojans unless they are reintroduced after installation.

Spyware: Spyware is designed to gather information about a person or organization without their knowledge. Like Trojans, spyware should be removed with an OS reinstallation unless it is reintroduced in some way.

Rootkit: Rootkits are designed to enable continued privileged access to a computer while actively hiding their presence. While a rootkit could potentially survive an OS reinstall if it infects the firmware or certain areas outside the OS, the scenario described points more specifically to a boot sector virus, especially considering the immediate return of the infection after OS reinstallation.