The 16 and 24 are analog mixers with an on-board digital recorder. So they have analog specs.
According to the specs in the OM, with faders and other volume controls set to unity gain (not maxed out), at unity gain the Main Out has an S/N of -80 dB. That means 99.9% of the time, the internal electronic white noise hiss of the unit will be masked easily and completely by material recorded at normal levels.
Any other type noise would be due most likely to cheap or defective cables, or RFI. External sources of RFI (including a computer - connected or not - or a computer monitor), and corrective steps are beyond the scope of this forum.
A
24/16/12 forum search turned up 4 pages of posts related to "noise", none of which were authoritatively found to be due to unit "defects". You may want to take a look at those also (click on the "Site Results" tab).
If the above have been conclusively ruled out, then a call or email to TASCAM support may be necessary. If so, a clearly stated, precise, detailed description of the issue, using TASCAM's terminology (not your own creations), and prepared in advance, will better enable the tech to make an assessment.