We address weak localization (WL) of electrons in a two-dimensional ballistic classically chaotic billiard of antidots, According to a recent proposal ballistic WL is sensitive to the transport relaxation and phase-coherence times as well as to the Ehrenfest time t(E) and to the Lyapunov exponent lambda of the classical system. This results in a non-trivial effect of the geometrical parameters of the antidots on the quantum WL correction to the classical magnetoconductivity. We analyze this phenomenon in detail and discuss how t(E) and lambda can in principle be determined from conductivity measurements.