Poor memory management can be considered as the first restrictive barrier to the implementation of the neutron transport equation for large reactors. The current research presents a new MRT with the ability to reduce the required memory and increase cache coherency. Also, given the high impact of the angular quadrature set used in the transport calculation, the effects of the angular set are investigated. As a reliable trial for an angular quadrature set examination, comparisons between the Forward and Adjoint transport calculations are performed.Three types of angular quadrature sets are adopted for our optimized MOC steady-state calculation. Based on two known constraints for the quadrature set evaluation, the accuracy and computational cost of the presented sets are examined. Satisfying these two conditions, our implemented Legendre-Chebyshev quadrature set with S20 angular order results in 7.0000E-06 and the 9.0000E-06 difference with reference Keff of G5G7 benchmark in the forward and adjoint calculation respectively. As well, our optimized parallel algorithm for MOC results in 6.18 speedup with 16 threads.