  A Lie (super)algebra with a non-degenerate invariant symmetric bilinear form
$B$ is called a nis-(super)algebra. The double extension $\mathfrak{g}$ of a
nis-(super)algebra $\mathfrak{a}$ is the result of simultaneous adding to
$\mathfrak{a}$ a central element and a derivation so that $\mathfrak{g}$ is a
nis-algebra. Loop algebras with values in simple complex Lie algebras are most
known among the Lie (super)algebras suitable to be doubly extended. In
characteristic 2 the notion of double extension acquires specific features.
  Restricted Lie (super)algebras are among the most interesting modular Lie
superalgebras. In characteristic 2, using Grozman's Mathematica-based package
SuperLie, we list double extensions of restricted Lie superalgebras preserving
the non-degenerate closed 2-forms with constant coefficients. The results are
proved for the number of indeterminates ranging from 4 to 7 - sufficient to
conjecture the pattern for larger numbers. Considering multigradings allowed us
to accelerate computations up to 100 times.
