What JT built is great and works well. Some people use half inch hardware cloth for the bottom, then put the astro turf mat on top of the hardware cloth.
That allows a lot of the dirt and debris the chickens track into the box, to filter down through the mat and hardware cloth, and onto the ground, both are designed to allow stuff through.
JT just takes out his mat once in a while and shakes it.
I can't remember if he did it with his, but with his system, you could also leave a one inch open slot across the whole front of the box, where the chickens come in, and when you take out the the mat, or even if you don't take out the mat, just use a whisk brush, to brush any dirt, or heaven forbid, poop, into the open slot, and onto the ground. The slot is way too small for an egg to fall through, or to bother the chickens.