Final answer:
For the longest cable run in a 10GBase network, 10GBaseER is the specification that should be selected as it supports distances up to 40 kilometers on single-mode fiber.
Step-by-step explanation:
When implementing a 10GBase network and aiming for the longest cable run, the best specification to choose is 10GBaseER. This specification stands for 10 Gigabit Ethernet Extended Reach and it allows for cable runs up to 40 kilometers (approximately 24.85 miles) when using single-mode fiber. To compare, 10GBaseLR (Long Reach) supports distances up to 10 kilometers (approximately 6.21 miles), 10GBaseSR (Short Reach) is designed for short distances up to 300 meters (approximately 984 feet) with multi-mode fiber, and 10GBaseLX4 uses wavelength-division multiplexing to provide a range of up to 10 kilometers but does so across four wavelengths on the same fiber strand.