Why not q/16 or q/4? And the implementation of AND is achieved by the following method. If q/16 is used with the appropriate OFFSET value, can’t it be used to implement multiple input AND gates?
I don’t know from where the table comes from, but perhaps it has to do with Section 4.1 of DM14
Yes, q/16 (or more generally, other values than q/8) can be used either to support multi-input gates or support larger plaintext modulus. Both extensions of the original DM scheme are supported in OpenFHE. For example, there are parameter sets that support 3-input and 4-input gates.