Public work is best
'best' is the definition.
('outdo' can be a synonym of 'best')
'public work' is the wordplay.
'public' becomes 'out' (I've seen this before).
'work' becomes 'do' ('do work' can be a synonym of 'work'**).
'out'+'do'='OUTDO'
'is' acts as a link.
(Other definitions for outdo that I've seen before include "Go one beter than, surpass" , "Exceed" , "Cap" , "Perform better than, be superior to" , "Beat" .)
(Other definitions for overtop that I've seen before include "Excel" , "best" , "Exceed in height" , "Surpass (one may go " ____ the ___")" , "Rise above" .)