An error model with asymmetric single error with magnitude four is considered. In this paper, the constructions of codes correcting single error of magnitude four over \mathbb Z2a3brare studied which is equivalent to construct B1[4](2a3br) sets. Firstly, we reduce the construction of a maximal size B1[4](2a3br) set for a ≥ 4 and gcd(r,6)=1 to the construction of a maximal size B1[4](2a-33br) set. Furthermore, we will show that maximal size B1[4](8·3br) sets can be reduced to maximal size B1[4](3br) sets and also give lower bounds of maximal size B1[4](12r) and B1[4](2·3br) sets. Finally, we give a necessary and sufficient condition on the existence of perfect B1[4](p) set for prime p.

Limited magnitude asymmetric error model is well suited for flash memory. In this paper, we consider the construction of asymmetric codes correcting single error over Z2krwhich is based on so called B1[4](2kr) set. In fact, we reduce the construction of a maximal size B1[4](2kr) set for k ≥ 3 to the construction of a maximal size B1[4](2k-3r) set. Finally, we give an explicit formula of a maximal size B1[4](4r) set and some lower bounds of a maximal size B1[4](2r) set. By computer searching up to q ≤ 106, we conjecture that those lower bounds are tight.