Try the Potato Silos. 3'? circles of 24"H chickenwire -- mine are squashed into 2'x4' semi-circles against the fence. 5 seed potatoes/silo.
The ground underneath was solid compacted clay subsoil lawn. Forked, soaked, piled with grass clippings/weeds, unfinished compost, cardboarded, then soaked again. Chickenwire circles secured in place, then piled with HAY *not* straw, more grass clippings, and straw. X's cut into the cardboard and seed potatoes snuggled into the moist ground below. Mulched with more hay, occasionally compost, and grass clippings as the potato plants grew.
BEST yield ever.
Only problem was that chipmunks discovered the potatoes and started eating them underground* -- probably lost about 1/2 dozen good potatoes
*I'm concerned for my sweet potatoes, some of which are planted in the same area. I should probably try digging around a bit, though I really need to wait until at least the end of the month for good potato development.