Selectively doped three period Al0.2Ga0.8As/GaAs structures have been grown by molecular beam epitaxy and characterised by Hall effect over a temperature range of 10 K–300 K. Electron mobilities as high as 211 000, 95 800 and 6700 cm2V−1s−1 have been obtained at 10 K, 78 K and 300 K, respectively. The total charge concentration in all the structures was about 2.25×1012 cm−2. These extremely high electron mobilities are a result of separating the donors and the electrons appreciably, and very-high-quality interfaces. To date, the figures at 78 K are the highest reported, while the 10 K figures are about twice the best previously reported results.