Gauge field corrections to 11-dimensional supergravity via dimensional reduction

Using the fact that eleven-dimensional supergravity yields type IIA supergravity under dimensional reduction on a circle, we determine higher-derivative terms of 11-dimensional supergravity including the $R^4$, $(\mathrm{\partial }{F}_4{)}^2{R}^2$ and $(\mathrm{\partial }{F}_4{)}^4$ terms.