We found this great growing guide on how to grow 100lbs of potatoes in 4 square feet on the Irish-Eyes Garden Seeds website. It was so intriguing, escpecially for the home gardener with limited space,
THE CAGE METHOD
Grow a few potato plants, each or in their own wooden box, crib, barrel or wire cage. The container should be about 18x18 inches at the base, about 24-30 inches tall, and able to be gradually filled with soft soil or mulch as the vines grow. Set each container atop a well-prepared fertile soil. Plant one strong seed piece and cover lightly with 4 inches of soil. As the vines grow, gradually fill the container with mellow compost, mulch or soil, but always make sure you don't cover more than one-third of the vine's new growth. With some varieties, the underground stolons which produce potato tubers keep on forming new ones for some time. In containers the yield may be increased 200-3000 percent compared with open-field culture. This is a great way to grow a lot of potatoes in a very limited space. We recommend doing this with Yellow Finn, Indian Pit, Red Pontiac, or the fingerling types. Watering requirements will be greater however, so check the cages or containers frequently in warm weather.
You will need:
6 - 2"x6"x8' *boards
1 - 2"x2"x10' *board
96 - 2½" wood screws
* - You can use pine, cedar, redwood or pressure treated mud sill that has been treated with copper sulfate, which is not toxic to the soil.
Cut 2"x2"s into 4 - 33" lengths.
Cut 2"x6"s into 12 - 21" lengths and 12 - 24" lengths.
Step 2 : Assemble as shown in figure 1.
HINT: Pre-drill screw holes in 2"x6"s.
Over prepared soil you will only build your box one board high. Fill with soft soil or mulch and plant seed potatoes 4" deep. As the vines grow approximately 12" above soil add another board and fill with soil being careful not to cover more than 1/3 of the vine. Keep repeating the process until the box is completed as shown in figure 2.
Step 3 :
Harvest Time! As shown in figure 3 remove screws on bottom board and harvest your oldest potatoes first. Replace soil and boards. Your next harvest will be layer #2 and so on until you reach the top board.