Very tight embeddings of subspaces of \(L_p\) for \(0<p<1\)

For \(0 1\), every \(d\)-dimensional subspace of \(L_p\) embeds linearly into \(\ell_p^{\lfloorμd\rfloor}\) with distortion at most \(C(p,μ)(\log(d+2))^{1/p}\). If its Rademacher type \(q\) constant is at most \(T\), where \(p<q\leq2\), the distortion is at most \(C(p,q,μ)T\), independ