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Mahmoodian and Soltankhah $\cite{MMS}$ conjectured that there does not existany $t$-$(v,k)$ trade of volume $s_{i}< s <s_{i+1}$, where$s_{i}=2^{t+1}-2^{t-i}, i=0,1,..., t-1$. Also they showed that the conjectureis true for $i=0$. In this paper we prove the correctness of this conjecturefor Steiner trades.

On the non-existence of some Steiner $t$-$(v,k)$ trades of certain volumes