We have performed extensive simulations to explore the possibility of detecting eclipses and transits of close , sub-stellar and planetary companions to white dwarfs in WASP light curves .
Our simulations cover companions \sim 0.3 \hbox { $ \thinspace R _ { \oplus } $ } < { R } _ { pl } < 12 \hbox { $ \thinspace R% _ { \oplus } $ } and orbital periods 2 { h } < P < 15 { d } , equivalent to orbital radii 0.003 { AU } < a < 0.1 { AU } .
For Gaussian random noise WASP is sensitive to transits by companions as small as the Moon orbiting a \textrm { V } \simeq 12 white dwarf .
For fainter white dwarfs WASP is sensitive to increasingly larger radius bodies .
However , in the presence of correlated noise structure in the light curves the sensitivity drops , although Earth-sized companions remain detectable in principle even in low S/N data .
Mars-sized , and even Mercury-sized bodies yield reasonable detection rates in high-quality light curves with little residual noise .
We searched for eclipses and transit signals in long-term light curves of a sample of 194 white dwarfs resulting from a cross-correlation of the McCook \& Sion catalogue and the WASP archive .
No evidence for eclipsing or transiting sub-stellar and planetary companions was found .
We used this non-detection and results from our simulations to place tentative upper limits to the frequency of such objects in close orbits at white dwarfs .
While only weak limits can be placed on the likely frequency of Earth-sized or smaller companions , brown dwarfs and gas giants ( radius \approx \hbox { $ \thinspace R _ { \textrm { \tiny jup } } $ } ) with periods < 0.1 - 0.2 days must certainly be rare ( < 10 \% ) .
More stringent constraints likely requires significantly larger white dwarf samples , higher observing cadence and continuous coverage .
The short duration of eclipses and transits of white dwarfs compared to the cadence of WASP observations appears to be one of the main factors limiting the detection rate in a survey optimised for planetary transits of main sequence stars .