Atomic data are important in astrophysical applications and transition rates can be used in the determination of element abundances and plasma diagnostics. To provide for the extensive data needs a number of general computer codes such as SUPERSTRUCTURE, CIV3, and ATSP2K have been developed. As an alternative to these codes, which all rely on the Breit-Pauli approximation, the fully relativistic GRASP2K code can be used. GRASP2K is based on the multiconfiguration Dirac-Hartree-Fock method and implements a bi-orthogonal transformation method that permits initial and final states in a transition array to be optimized separately, which, in many cases, leads to more accurate values of the resulting rates. The GRASP2K package also contains modules to compute diagonal and off-diagonal hyperfine interaction constants, isotope shifts, Land´e gJ factors, and splittings of magnetic sub-state in intermediate and strong magnetic fields. In this work, GRASP2K has been applied to provide highly accurate spectroscopic data for ions in the Ne-like sequence between Mg III and Kr XXVII. Valence, core-valence, and core-core correlation effects were accounted for through SD-MR expansions to increasing sets of active orbitals. In Mg III, Al IV, Si V, P VI, S VII, and Ar IX, for which experimental energies are known to high accuracy, the mean error in the calculated energies is only 0.011%. For ions with no available experimental energy levels the calculated values should be most valuable in various applications. The high accuracy of the calculated energies makes it possible, in some cases, to to point out experimental values that are in error. Babushkin (length) and Coulomb (velocity) forms of transition rates are computed and agree to within a few percent for the majority of the allowed transitions. Computed lifetimes for states belonging to the 2p33s and 2p53d configurations are in good agreement with values from beam-foil measurements as well as from accurate MCHF Breit-Pauli calculations.