New simple Lie superalgebras in characteristic 3

Symplectic (respectively orthogonal) triple systems provide constructions of Lie algebras (respectively superalgebras). However, in characteristic 3, it is shown that this role can be interchanged and that Lie superalgebras (respectively algebras) can be built out of symplectic triple systems (respectively orthogonal triple systems) with a different construction. As a consequence, new simple finite dimensional Lie superalgebras, as well as new models of some nonclassical simple Lie algebras, over fields of characteristic 3, will be obtained.