Recently the Itchmo main site had a review of high-sided litter boxes, both commercial ones and make-your-own. The problem being addressed was cats who spray while standing in the box. I want to report that I got a high-sided box last week, and this has solved a long-standing problem for me: litter piles on the floor.
Two of my cats are real excavators in the litter box. They seem to delight in scooping piles
of litter out onto the floor. Then another cat comes along, says "Oh, litter!" and uses the litter on the floor
... you can see why I used a lot of enzyme deodorizer, etc. I have tried boxes with curved-in top edges, many, many types of pads, plastic bags, newspaper, lids of plastic storage boxes, etc., and never found anything that worked to keep the litter piles and the "results" off my floors.
I was not able to find the Rubbermaid box referred to in the Itchmo article, but I did find the Catty Corner Extra-Large High-Sided corner litter pan. This product was labelled as made in the USA, and has worked wonderfully! It is a nice, big, roomy box with high sides that seem to foil even my most vigorous earth-movers. There is a lower cut-out entry space that I think would be low enough for a geriatric cat, but maybe not for a kitten. The box also comes with a matching litter catcher mat that goes outside the entry to catch and contain in that area. Although the mat is made from the same stiff plastic as the box, my cats show no hesitation in stepping on it, unlike many other plastic objects. I was not able to find this item in an online search, only a covered version which some cats might object to. But it is worth checking in stores for availability.