The field SERIAL works for registered users (standalone Desktop users) and not with Server. But you may use the NTSID or NTDOMAINSID and NTNAME fields instead.
Even better and simpler, set a password to your file using the field PASSWORD. If any other user that is not in the section list and knows the password will not be granted access.
Check this document on further examples on how to use section access and its different fields.
Hope that helps.