I created the stl file in the windows 10 3d builder program by subtracting from the box a sheet of hexagons that I'd created in scad. The simple box file is included as well.
I've now written an scad file that produces the equivalent box and should be customisable.
I've printed this ok with no supports.
I've printed the stl file uploaded here and an stl file produced from the scad file. I use simplify 3d for slicing and got best results by making sure that "Apply bridging settings to perimeters" is enabled and the unsupported area threshold is set low enough to bridge the top of the cutouts.
I'd been looking for a box with cutouts and was inspired by the honeycomb cutouts used in https://www.thingiverse.com/thing:21593. The initial model I made was based on the cutouts used for the lid but I gradually moved towards full scad as I couldn't get everything lined up properly in 3d builder.
I use simplify3d and print a skirt of 2 layers, 20 outlines, 0mm from the part. This helps stop the corners curling up on my printer.
It takes around 14 hours to print off the 8x8x10 model, around 21430mm / 64.43g of plastic.
I'm using PLA.