  We prove that no $14$-connected (resp. $30$-connected) stably parallelizable
manifold $N^{30}$ (resp. $N^{62}$) of dimension $30$ (resp. $62$) with the
Arf-Kervaire invariant 1 can be smoothly embedded into $\mathbb{R}^{36}$ (resp.
$\mathbb{R}^{83}$).
