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An error model with asymmetric single magnitude four error is considered.This paper is about constructions of codes correcting single error over$\mathbb{Z}_{2^{a}3^{b}r}$. Firstly, we reduce the construction of a maximalsize $B_{1}[4](2^{a}3^{b}r)$ set for $a\geq4$ and $\gcd(r,6)=1$ to theconstruction of a maximal size $B_{1}[4](2^{a-3}3^{b}r)$ set. Further, we willshow that maximal size $B_{1}[4](8\cdot3^{b}r)$ sets can be reduced to maximalsize $B_{1}[4](3^{b}r)$ sets. Finally, we give a lower bounds of maximal size$B_{1}[4](2r)$ and $B_{1}[4](2\cdot3^{b}r)$ sets.

Correcting Codes for Asymmetric Single Magnitude Four Error