Hi
I've mainly found the following on Ancestry records and trees and therefore not necessarily substantiated:
Herbet Nune, b. abt 1566, Wortham.
Married Christina Battelye abt 1593, Wortham.
Herbets' parents are likely to be William Nunn 1543-1604 and Joan Punchard 1535-1597.
William Nunn & Joan Punchard, Rattlesden 1564, mar.
There are possible deaths in the NBI for William and Joan:
28 Jan 1603, William Nunne, Oakley St Nicholas, bur.
20 Oct 1597, Joan Nune, Rattlesden St Nicholas, bur.
Williams' NBI death date differs from others.
There are quite a number of Nune's in the area, notwithstanding name variants, e.g. Great Whelnethen, Oakley, Rattlesden, Bury St Edmonds and Felsham where William may have been born.
I hope there may be something there that will give you a lead.
Regards
Geoff