FYI: OSB or any other solid board under a mattress is 'in general' not a great idea. Its likely OK for a short term fix (couple of months), but not recommended for long term use.
Anyone who has purchased a box spring, especially the more recent versions is left wondering what has happened to the springs. Today's box spring look to be little more than an expensive spacer. In the past, they provided additional support for the mattress and the human above, and they where a very important part of the overall comfort and long life of the mattress. Today's mattresses are far more self-supporting, i.e. they do not require the additional 'spring support' of the old style box spring. So, why invest in a box spring? As in the past, today's box spring provide much needed ventilation at the bottom the mattress to allow passive movement (gravity) of naturally occurring moisture from the bottom of the mattress. Using a solid surface under a mattress halts this 'venting' and will result in a build-up of moisture in the mattress.
In short, if you do not want to purchase a box spring or the height you want will be to tall if you use one - use plank cross boards, not a solid board.
If you have purchased a high-end mattress, you really do need a matched box spring to assure their long life. If not, you just wasted a lot of money and will be back buying a new mattress in about half the stated normal life.