R^4 Corrections to Eleven Dimensional Supergravity via Supersymmetry
  By applying Noether method to N=1 local supersymmetry in eleven dimensions, we obtained two candidates of R^4 corrections to the supergravity. The bosonic parts of these two completely match with the results obtained by type IIA string perturbative calculations. We also obtained 13 parameters which relate only fermionic terms. 
Yoshifumi Hyakutake and Sachiko Ogushi