  The largest Key Science Program of the RadioAstron space VLBI mission is a
survey of active galactic nuclei (AGN). The main goal of the survey is to
measure and study the brightness of AGN cores in order to better understand the
physics of their emission while taking interstellar scattering into
consideration. In this paper we present detection statistics for observations
on ground-space baselines of a complete sample of radio-strong AGN at the
wavelengths of 18, 6, and 1.3 cm. Two-thirds of them are indeed detected by
RadioAstron and are found to contain extremely compact, tens to hundreds of
$\mu$as structures within their cores.
