In most current professional indoor antenna measurement systems, the far-field distance is often too large for a practical shielded and anechoic chamber; hence, the measurement is done in the near field region, and the collected data computationally processed to yield the desired far field pattern; this process is called the "Near-Field to Far-Field transformation". The cost of a measurement is proportional to the number of samples to be measured; the minimum number of necessary samples is ruled by a result equivalent to the sampling theorem for signals, and usually called the Nyquist limit. In this work, the number of necessary near-field samples is reduced beyond the Nyquist limit by adding information on the geometry of the antenna under test (AUT), and by simulations of parts of the AUT.