  Our recent study [Phys. Rev. B 103, 085309 (2021)] verified the existence of
$\bf{k}$-linear Rashba spin-orbit coupling (SOC) of two-dimensional hole gases
in quantum wells (QWs) which originates from a combination of
heavy-hole-light-hole (HH-LH) mixing and direct dipolar coupling to the
external electric field. However, the Rashba SOC dependence on QW orientations
remains unclear. Here, we explore this dependence on QW orientations and
uncover an upper and lower bound to the orientation-dependent $\bf{k}$-linear
Rashba SOC along the [110]- and [111]- crystalline directions by performing
atomistic pseudopotential calculations associated with theoretical analysis.
The intrinsic HH-LH mixing at the Brillouin zone center, maximal in
[110]-oriented quantum wells and minimal in [111]- and [001]-oriented QWs,
plays an essential role. Remarkably, we find that only $\bf{k}$-cubic Rashba
SOC exists in [111]-oriented QWs. These findings help understand the physical
mechanism of the Rashba SOC dependence on QW orientations and provide a
strategic prediction for experiments to realize the large Rashba SOC.
