How big of a container for king oyster mushrooms?

I have some king oyster mushroom mycelium that I got from a kit, raised to fruition, and then tried to propagate on cardboard.  I got a few sheets of boiled and soaked cardboard and put it in a dish and now it’s all coated with mycelium.  It’s just a few sheets, though - 3 small sheets of mycelium in a dish.  Is that enough for mushrooms or should I add more and put it in a bigger container?  

EDITED:
For every 5lbs of dry cardboard you will get 1lbs of mushroom harvest, under ideal lab conditions according to Paul Stamets "Growing Gourmet and Medicinal Mushroom pg 306" . So use that 5:1 ratio, to help guide how much fresh cardboard/woodchip you need. Seeing as how you and I aren't Paul Stamets, we should probably use a ratio of 10:1

Thank you!

What I do is use the cardboard to inoculate paper kitty litter prepared to 65% moisture content using boiled water. Once colonized I use the kitty litter to spawn bulk substrate like staw, chips or sawdust.