Classification of linearly compact simple N=6 3-algebras

$N\leq 8$ 3-algebras have recently appeared in N-supersymmetric 3-dimensional Chern-Simons gauge theories. In our previous paper we classified linearly compact simple N = 8 n-algebras for any $n \geq 3$. In the present paper we classify linearly compact simple N = 6 3-algebras, using their correspondence with simple linearly compact Lie superalgebras with a consistent short Z-grading, endowed with a graded conjugation. We also briefly discuss N = 5 3-algebras.