Classification of linearly compact simple algebraic N = 6 3-algebras

N ≤ 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 ≥ 3. In the present paper we classify algebraic linearly compact simple N = 6 3-algebras over an algebraically closed field of characteristic 0, using their correspondence with simple linearly compact Lie superalgebras with a consistent short ℤ-grading, endowed with a graded conjugation. We also briey discuss N = 5 3-algebras.