There are several ways to form the base of a chest. The simplest option is a piece of sheet good such as plywood... but at the love of wood we prefer solid timber. The problem with solid timber is that it expands and contracts as the humidity changes. Any design needs to take this into consideration or come a humid season your box will fall apart!
There are several options to use solid timber. A useful and recent article in Fine Woodworking nicely explained using solid timber in a frame and panel method.
Another method is to use 3-4" strips in a tongue and groove or slip matched fashion. This is the technique I used for the shelf on the roubo bench.
The bases for the Christmas Boxes are made by a single piece of radiata pine held captive (free of glue but floating constrained) in a groove around the case. After cutting to size, tongue and groove were formed with the small plow plane.