In this study, we optimize the nonreciprocal transmission of surface acoustic waves (SAWs) in a piezoelectric/ magnetic heterostructure loaded with a CoFeB(d A )/Ru(0.55 nm)/ CoFeB(d B ) synthetic antiferromagnet (SAF). The SAF is composed of two ferromagnetic layers separated by a thin nonmagnetic Ru spacer layer, providing strong antiferromagnetic interlayer exchange coupling. The optical spin wave (SW) mode shows a large nonreciprocal dispersion relation in conjunction with a narrow line width. Therefore, for oppositely propagating SAWs, the SAW-SW resonances can become fully separated. For the optimized CoFeB(16 nm)/Ru(0.55 nm)/CoFeB(5 nm) SAF, we demonstrate both, a giant nonreciprocal SAW transmission of ΔS ± /l f > 250 dB/mm and a very low magnetoacoustic insertion loss of IL Δ /l f < 1 dB/mm per length l f of the SAF in the acoustic path at frequencies above 5 GHz. These results yield the potential for the realization of novel microwave devices with nonreciprocal signal transmission, such as acoustic isolators. In addition, the experimental results are in excellent agreement with a phenomenological model that considers the dipolar fields of the SWs and takes the bilinear and biquadratic interlayer exchange coupling into account.