Quasi-optimal amplitude distributions for antenna arrays are proposed that provides any specified minimum level of side-lobes. The distribution is implemented for a given number N of radiating elements by truncating a binomial distribution for some large number n of virtual radiators. Radiation patterns, gain, main lobe beamwidth and scattering coefficients of antenna arrays are calculated when changing number of real and virtual radiators and spacing between them in a wide range. It was shown that the directivity characteristics of the truncated binomial arrays are intermediate between the characteristics of binomial and uniform antennas.