The Schur multipliers of finite simple groups are known and easily accessible: https://en.wikipedia.org/wiki/List_of_finite_simple_groups

Moreover, as a consequence of the second Whitehead's Lemma, if $L$ is a finite-dimensional simple Lie algebra over a field $\mathbb{F}$ of characteristic zero, then its Schur multiplier $H_2(L, \mathbb{F})$ is trivial. This is no longer true in positive characteristic. Now, according to the Block-Wilson-Strade-Premet classification, every simple finite-dimensional Lie algebra over an algebraically closed field of characteristic p > 3 is of classical, Cartan, or Melikian type. For my purposes, I would appreciate if I could have need any information or possible references about the following:

QUESTIONIs there any explicite description of $H_2(L,\mathbb{F})$, where $L$ is a finite-dimensional simple Lie algebra over an algebraically closed field $\mathbb{F}$ of characteristic $p>3$?

I am mainly interested in the case in which $L$ is a restricted simple Lie algebra of Cartan type.