We report high resolution self-consistent field theory (SCFT) calculations that show the gyroid phase, Q230, to be stable in conformationally symmetric linear diblock copolymer melts prepared within the strong segregation regime, cN = 100, over a composition window of ~ 1.5%. This window broadens with the introduction of conformational asymmetry. The SCFT equations were solved using a novel pseudospectral approach with a plane wave basis and periodic boundary conditions. Saddle point field configurations were obtained using a semi-implicit Seidel relaxation algorithm. The modified diffusion equation was solved using a fourth-order backward differentiation formula and implicit treatment of the Laplacian operator. Our calculations are consistent with recent experimental observations of Q230 in strongly segregated diblocks.