The paper presents results from a small survey of 22 young, nearby stars that was designed to detect substellar companions and ultimately giant extrasolar planets down to Jupiter masses. The targets are members of the Tucana and Beta Pictoris moving groups apart from the somewhat older star HIP 71395 that has a radial velocity trend suggesting a massive planet in large orbit. The survey was carried out in the L-band using adaptive optics assisted imaging with NAOS-CONICA (NACO) at the VLT. The chosen observation wavelength is well suited to search for close companions around young stars and delivers unprecedented detection limits. The presented technique reaches some of the best sensitivities as of today and is currently the most sensitive method for the contrast limited detection of substellar companions that are cooler than about 1000K. The companion to 51 Eri, GJ 3305, was found to be a very close binary on an eccentric orbit. No substellar companions were found around the target stars, although the method permitted to detect companions down to a few Jupiter masses at orbital distances of typically 5 astronomical units. A planet with a mass >1 M_Jup at distances >5 AU around AU Mic can be excluded at the time of our observations. The absence of detected planets sets constraints on the frequency distribution and maximum orbital distance of giant exoplanets. For example, a radial distribution power law index of 0.2 in combination with a maximum orbital radius exceeding 30 AU can be rejected at a 90% confidence level.
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