The most common cause of Office 2016 error 0-1028 is a previous install of Office 2013/365 or older versions.
To fix this error we would need to remove all traces of previous office versions; luckily Microsoft has a utility for this purpose specifically.
To begin; download the O15CTRRemove.diagcab
a) Run it; and continue with instructions on screen.
b) Wait for it to finish uninstalling Office 2013.
c) Then hold windows key and press R and key in the following path:
C:\Program Files\Common Files\Microsoft Shared\
d) Locate the folder called ClickToRun and delete/remove it.
e) Now try to install Office 2016 and it will install fine.