Place two 2-by-4-by-16-inch boards parallel to each other on a work surface. Orient the boards vertically. The 2-by-16-inch sides should be resting flat on the work surface. Space the boards 17 1/2 inches apart from the inside edges. Repeat this process with the remaining two 2-by-4-by-16-inch boards so that you have two pairs. These are the uprights for the brackets.
Insert one 2-by-4-by-17 1/2-inch board between the bottom ends of each pair of uprights. Rest the 2-by-17 1/2-inch sides flat on the work surface. The 2-by-4-inch ends should be flush with the inside edges of the uprights. These are the bottom supports for the brackets.
Drive two evenly spaced 3-inch wood screws through the uprights into the ends of the bottom supports at each joint using a screw gun. You should now have two u-shaped bracket assemblies.
Select a location for the brackets on the basement ceiling. They will require a 36-inch long space and take up the width of two floor joists. Slide the top ends of the uprights in one bracket assembly over the outside edges of the two floor joists at one end of the selected 36-inch span. Drive four evenly spaced 3-inch wood screws through the outside of the uprights into the floor joists using a screw gun. Repeat this process to secure the second bracket assembly on the opposite end of the 36-inch span.
Slide the plywood panel between the inside edges of the bracket uprights. Rest the panel flat on the top sides of the bottom supports. Drive 1 1/2-inch wood screws through the ends of the plywood panel into the bottom supports with a screw gun every 2 inches to secure it in place. The plywood panel acts as a shelf for the brackets so that you can place storage items on top of it.