Hi Connie,
Thank you for reaching out.  It would be fine to lay your freshly dug potatoes on a tarp in your shed.  It is important that the potatoes stay in a cool, dry, dark area that is free of pests (like mice).  you can also store them in a crate or a box in the shed, root cellar or in a basement that will stay cool and dark.  

Here is a link to more information on storing potatoes: https://extension.oregonstate.edu/news/tips-keeping-harvested-potatoes-fresh