A note on decomposition numbers of G2(2n)

The decomposition numbers of the finite Chevalley group G2(pn) of type (G2) defined over a finite field of characteristic r which divides pn+1 are almost determined by [G. Hiss, J. Algebra 120 (1989) 339–360]. I will prove that the decomposition numbers are bounded independently of pn by using the same argument as in [T. Okuyama, K. Waki, J. Algebra 199 (1998) 544–555] in case of p=2.