We prove the validity of the freeness conjecture of Brou\'e, Malle and Rouquier for the generic Hecke algebras associated to the exceptional complex reflection groups of rank 2 belonging to the tetrahedral and octahedral families, and we give a description of the basis similar to the classical case of the finite Coxeter groups.
Decomposition matrices for the generic Hecke algebras on 3 strands in characteristic 0
On the cyclotomic Hecke algebras of complex reflection groups
The BMR symmetrising trace conjecture for groups $G_4,\,G_5,\,G_6,\,G_7,\,G_8$
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