Answer:
The database on a mobile device containing bands, sub-bands, and service provider IDs that allow the device to establish a connection with the right cell phone tower is called a "Preferred Roaming List" (PRL).
Step-by-step explanation:
The PRL is a database maintained by the mobile network operator (MNO) and stored on the mobile device. It contains information about the bands and sub-bands supported by the MNO's network and the service provider IDs of roaming partners. When a mobile device is searching for a signal, it consults the PRL to determine which network frequencies and towers are available and compatible with the device.
The PRL is periodically updated by the MNO to reflect changes in network coverage and roaming agreements. Updates to the PRL can be pushed to the device over-the-air (OTA) or manually installed through a software update or by calling the carrier's customer service.