The majority of stars both host planetary systems and evolve into a white dwarf ( WD ) .
To understand their post-main-sequence ( PMS ) planetary system evolution , we present a search for transiting/eclipsing planets and other Substellar Bodies ( SBs ) around WDs using a sample of 1148 WDs observed by K2 .
Using transit injections , we estimate the completeness of our search .
We place constraints on the occurrence of planets and substellar bodies around white dwarfs as a function of planet radius and orbital period .
For short-period ( P < 40 days ) small objects , from asteroid-sized to 1.5 R _ { \earth } , these are the strongest constraints known to date .
We further constrain the occurrence of hot Jupiters ( < 1.5 \% ) , habitable zone Earth-sized planets ( < 28 \% ) , and disintegrating short-period planets ( \sim 12 \% ) .
We blindly recovered all previously known eclipsing objects , providing confidence in our analysis , and make all light curves publicly available .