When asking cats to use a litter box, you are teaching against their instincts. It's no surprise that the most common behavior problem reported by cat owners is urination and defecation outside the litter box.
To minimize the chances that your cat will christen the Persian rug, keep in mind the habits of wild cats:
A good "rule of paw" is to have one litter box available for each cat, plus one extra. Litter boxes should be placed in accessible areas - avoid dark, damp basements, distant bedrooms, or areas unprotected from the noises of washing machines, furnaces, traffic, and the like.
To accommodate the preference for open spaces (and dislike for odors), avoid covered litter boxes. Instead, use as large and as open a box as possible. A study of texture preferences has shown that cats prefer the clumping, scoopable litters to other types.
Finally, try to keep your litter boxes as clean as possible, removing urine and feces at least daily. Also, place thick vinyl on those areas outside the litter box that your cat has been using.
After cleaning with a urine odor-neutralizing product, it also is helpful to top the vinyl with items that smell clearly unpleasant to cats. Cats dislike odors such as cedar chips, perfumes, and citrus oils. If these measures are thorough, even the most challenging cat can be taught to use the litter box.