As Quincy56 mentioned the the minimum disk count is for vault devices which are on the first 4 disks of each directly attached DAE. The logic is, 32 disks are required for each director pair. So I assume you have 3 director pairs. Also don't forget to add disks for spares.
Is there any logic behind the minimum drive requirement on DMX ?
Why we need minimum 96 drive to start up a DMX4 Storage Frame?