$\mathsf{DTime}(O(n^k)) \subseteq \mathsf{NTime}(g)$ for some $g \in o(n^k)$?
It seems to me that you are not familiar with the basic complexity theory and therefore your question is probably not suitable for cstheory.

You probably mean to ask if the following statement is true:


  $\mathsf{DTime}(O(n^k)) \subseteq \mathsf{NTime}(g)$ for some $g \in o(n^k)$.


Note that the $\mathsf{NTime}$ hierarchy theorem is tight. If the answer to your question was positive then it would separate $\mathsf{NTime}$ from $\mathsf{DTime}$ which is not known as explained in the answers to the question linked by Robin.