Dimension Formulae in Genus Zero and Uniqueness of Vertex Operator Algebras

We prove a dimension formula for orbifold vertex operator algebras of central charge 24 by automorphisms of order n such that Gamma(0)(n) is a genus zero group. We then use this formula together with the inverse orbifold construction for automorphisms of orders 2, 4, 5, 6, and 8 to establish that each of the following fifteen Lie algebras is the weight-one space V-1 of exactly one holomorphic, C-2-cofinite vertex operator algebra V of CFT type and central charge 24: A(5)C(5)E(6,2), A(3)A(7,2)C(3)(2), A(8,2)F(4,2), B8E8,2, A(2)(2)A(5,2)(2)B(2), C8F42, A(4,2)(2)C(4,2), A(2,2)(4)D(4,4), B5E7,2F4, B4C62, A(4,5)(2), A(4)A(9,2)B(3), B6C10, A(1)C(5,3)G(2,2), and A(1,2)A(3,4)(3).