This paper presents the construction of an explicit, optimal-access, high-rate MSR code for any (n, k) with d=k+1, k+2, or k+3 over the finite field $F_Q$  having sub-packetization $alpha =q^{lceil (n/q) rceil }$ where q = d−k+ 1 and Q = O(n). The sub-packetization of the construction meets the lower bound proven in a recent work by Balaji et al.. To our knowledge,  the codes presented in this paper are the first explicit constructions of MSR codes with d < (n − 1) having optimal sub-packetization, optimal access and small field size.