Necessary condition on smoothness parameter for Strichartz estimates

Question

It is well known that to holds Strichartz estimates for initial data in homogeneous Sobolev pace $\dot{H}^s (\mathbb R^d)$ i.e $\| |e^{it\Delta} f |^2 \|_{L^p _t L^q _x} \lesssim 1$, whenever $\| f \|_{\dot{H}(\mathbb R^d)} = 1$, it is necessary that $\frac{2}{p} + \frac{d}{q} = d - 2s $ and $s \in \,[0, \frac{d}{2})$. By scaling arguement I have able to deduce the condition $\frac{2}{p} + \frac{d}{q} = d - 2s $ and $s < \frac{d}{2} $ but unable to show that $s \geq 0$. How to get $s \geq 0$ ?