  The active K2V star $\epsilon$ Eri hosts the most nearby known extrasolar
planet. With an angular separation of about 1" on average, and an age of a few
to several hundred Myrs, $\epsilon$ Eri b is one of the prime candidates for
becoming the first definitive extrasolar planet imaged directly. We present a
multi-epoch deep differential imaging survey performed with NACO-SDI at the VLT
with the aim of finding the planet. The results are combined with recent
astrometry in an attempt to further constrain the detection limits. No
convincing candidate is found among the many coherent structures that
constitute the residual speckle noise, which is the dominant noise at small
angular scales. We present our detection limits, compare them with the
estimated brightness of $\epsilon$ Eri b, and analyze how the limits can be
improved further. It is found that integration time remains a very important
parameter for achieving good results, even in the speckle-dominated regimes.
The results yield new, improved upper 3$\sigma$ limits on the absolute H-band
(1.6 $\mu$m) brightness of the 1.55 $M_{\rm jup}$ companion of 19.1 to 19.5
mag, depending on the specific age of the system.
