The Great Desert was a “great sea of land” that lay north of Calormen and south of Archenland. It was also west of the uninhabited western country of the Western Wild and east of the Merpeople's sea nation by the Eastern Ocean. It was beyond the southern frontier of the Narnian Empire and was in the northern exterior of the Calormen Empire. It could be crossed by hard riding on horseback in the span of a night and a day.
The desert afforded the northern countries some protection from Calormen invasion, since the springs at the great oasis would not have been sufficient to enable an army of any size to cross it. A secret and well-watered valley that led into Archenland did exist, though its existence was unknown to the Calormenes, which forced them to rely on surprise attacks by relatively small cavalry forces. As no one from any state lived or operated there, it was, technically, an unruled state of its own. It is possible that the Oasis did house a few permanent and independent residents.