Even with his recollection of the sonic screwdriver lost with the rest of his memory, the Doctor retained enough residual knowledge to know how such a device could function. He attempted to recreate it in his spare time, but the limited technology of the time meant that the best he could accomplish was a device the size of a standard suitcase.
It was capable of holding objects within it to present the illusion of being a standard suitcase. The Doctor perfected the device between the early and mid-1980s, using it to open locked doors in a standard tower and even the door to the space shuttle Atlantis. The suitcase was eventually destroyed during the battle on the Supremacy. (PROSE: Father Time)