I am not super familiar with rack tub sizes typically used for ASF's, but I expect anything that is good for mice should work for them. Thus, height of the tub between 4-6" should be fine.

As for the size of the wire mesh, you need it to be small enough the lab blocks used don't fall through,and big enough to allow the rodents to chew at the food.

The taller tubs, over 6" are better for rats. Pretty much you want tubs as high as the body length of a weaned rodent, unless you intend to move weaned rodents into smaller tubs till they reach adult size.
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PHLdyPayne