Are there minimal exceptional aGUTs from stable 5D orbifolds?

In analysing five dimensional orbifolds with exceptional gauge groups, we seek to find stable vacua configurations which satisfy the minimal requirements for asymptotic grand unified models. In this respect we show that no minimal asymptotic grand unified theory can be built. Our results point towards non-minimal models based on E6: one featuring supersymmetry, and the other needing a modification of the Coleman–Weinberg potential to stabilise the breaking of E6 to the standard model gauge group.