High field de Haas-van Alphen measurements of RT$_{2}$Zn$_{20}$ (R=Yb and Lu,T=Fe, Co and Rh)*

The de Haas--van Alphen (dHvA) effect in heavy fermion compounds YbFe$_{2}$Zn$_{20}$, YbCo$_{2}$Zn$_{20}$ and YbRh$_{2}$Zn$_{20}$ as well as the nonmagnetic compounds LuFe$_{2}$Zn$_{20}$, LuCo$_{2}$Zn$_{20}$ and LuRh$_{2}$Zn$_{20}$ have been observed in pulsed fields up to 55 T directed along [110] and in the temperature range 0.4K to 12K. The cyclotron effective masses of~YbT$_{2}$Zn$_{20}$ (T=Fe,Co and Rh) range from 1.8m$_{0}$ to 2.8m$_{0}$. Self-consistent tight binding linear muffin-tin orbital method in the atomic sphere approximation (TB-LMTO-ASA) has been used to construct Fermi surfaces of LuT$_{2}$Zn$_{20}$(T=Fe, Co and Rh). The calculated dHvA frequencies show good agreement with the experiments.