On strings containing all subsets as substrings

Let S_π be the length of a shortest sequence of positive integers which contains every Y ?{1,…,n} as a subsequence of |Y| consecutive terms. We give the following asymptotic estimation: $\text{(}\text{2}\text{πn)}{}^{\mathrm{<mtext>1</mtext><mtext>2</mtext>}}\text{2}{}^{\mathrm{n}}\text{?S}{}_{\mathrm{n}}\text{?(}\text{2}\text{π)}\text{2}{}^{\mathrm{n}}$. The upper bound is derived constructively.