Classification of finite dimensional nilpotent Lie superalgebras by their multiplier

Let $L$ be a nilpotent Lie superalgebra of dimension $(m\mid n)$ and $s(L) = \frac{1}{2}[(m + n - 1)(m + n -2)]+ n+ 1 - \dim $\mathcal{M}$(L)$,where$$\mathcal{M}$(L)$denotestheSchurmultiplierof$L$\mathrm{.}Here$s(L)\geq 0$ and the structure of all non-abelian nilpotent Lie superalgebras with $s(L)=0$ is known((\cite{Nayak2019}). This paper is devoted to obtain all nilpotent Lie superalgebras when $s(L)\le 2$. Further, we apply those results to list all non-abelian nilpotent Lie superalgebras $L$ with $t(L)\le 4$.