Maximum accessible gain of an antenna

In known paper(1948), Chu ascertained that the bounds of antennas gain were depending from possibility of antenna matching to the spherical harmonics of field. Chu discovered the sequence of 2-Port circuits that were been equivalent to the spherical harmonics in this sense. Chu and authors of the further publications were usually limiting analysis to approximation of the 2-Ports by the resonant circuits. In this message, I offer the new algorithm for computation the extremal gain of the antenna that is enclosed in an imagined sphere and acts in the preassigned frequency band. The algorithm is based on the exact analysis of the constraints conditioned by the properties of the Chu 2-Ports. The results are correct for any antennas, in particular, for supergain ones.