When Goodby, Silverstein & Partners saw that Apple had sold 150,000 iPads before the device even went on sale, they saw an immediate and time-sensitive opportunity for its Sprint client.

“What we saw was an opportunity to tie a killer device to a pretty problematic network,” said Christian Haas, creative director and associate partner at the San Francisco-based Omnicom agency.

The device is Sprint’s Overdrive 3G/4G Mobile Hotspot, and the product the agency created to promote it is the 4G Case by Sprint, a custom-designed sleeve developed for the hot Apple product and other WiFi-enabled devices like Barnes & Noble’s Nook. An additional pouch houses Sprint’s Hotspot device, which allows users to connect using Sprint’s 4G network.

“We saw an opportunity for Sprint to ride this pop-culture wave and play on AT&T’s weakness, their network,” said Haas. “It’s almost like a Trojan horse.”

The device, Sprint claims, allows people to use their iPads at speeds 10 times faster than 3G. The case became available in select Best Buy stores this week. Through an exclusive arrangement with the retailer, Sprint is offering customers a free case with each purchase of the Overdrive.

The product is also featured in TV commercials asking, “What can you do with 4G?” One spot shows a man using the device with his laptop and cell phone in a variety of locations, like on a park bench or at an airport. Another ad shows a young man, with radio personality Casey Kasem at his side, using the device for speedy music downloads on his iPhone.

The case is the first product design to come out of Goodby. “The end result is about selling Overdrives,” said Haas. “We are not making money on the product. We are treating it as a marketing campaign.”