We investigated the Ising model on a square lattice with ferro and antiferromagnetic interactions modulated by the quasiperiodic Octonacci sequence in both directions of the lattice. We have applied the Replica Exchange Monte Carlo (Parallel Tempering) technique to calculate the thermodynamic quantities of the system. We obtained the order parameter, the associated magnetic susceptibility ($chi$) and the specific heat $(c)$ in order to characterize the universality class of the phase transition. Also, we use the finite size scaling method to obtain the critical temperature of the system and the critical exponents $beta$, $gamma$ and $ u$. In the low temperature limit we have obtained a continuous transition with critical temperature around $T_{c} approx 1.413$. The system obeys the Ising universality class with logarithmic corrections. We found estimatives for the correction exponents $hat{beta}$, $hat{gamma}$ and $hat{lambda}$ by using the finite size scaling technique.
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