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Abundant high-rate $(n, k)$ minimum storage regenerating (MSR) codes have been reported in the literature. However, most of them require contacting all the surviving nodes during a node repair process, resulting in a repair degree of $d=n-1$ . In practical systems, it may not always be feasible to connect and download data from all surviving nodes, as some nodes may be unavailable. Therefore, there is a need for MSR code constructions with a repair degree of $d < n-1$ . Up to now, only a few $(n, k)$ MSR code constructions with repair degree $d < n-1$ have been reported, some have a large sub-packetization level, a large finite field, or restrictions on the repair degree $d$ . In this paper, we propose a new $(n, k)$ MSR code construction that works for any repair degree $d>k$ , and has a smaller sub-packetization level or finite field than some existing constructions. Additionally, in conjunction with a previous generic transformation to reduce the sub-packetization level, we obtain an MDS array code with a small sub-packetization level and $(1+\epsilon)$ -optimal repair bandwidth (i.e., $(1+\epsilon)$ times the optimal repair bandwidth) for repair degree $d=n-1$ . This code outperforms some existing ones in terms of either the sub-packetization level or the field size.