\({\textbf {(1}}+ \varvec{\epsilon } {\textbf {)}}\) -optimal Maximum Distance Separable ( \({\textbf {1}}+\varvec{\epsilon } {\textbf {)}}\) -optimal MDS) codes, which are a special kind of \({\textbf {(n, k)}}\) MDS codes, can repair a single failed node by downloading slightly sub-optimal amount of data from \({\textbf {d}}\) helper nodes where \({\textbf {d}} \varvec{\in } {\textbf {[k, n)}}\) , and have small sub-packetization level. Some \({\textbf {(1}}+\varvec{\epsilon } {\textbf {)}}\) -optimal MDS codes have been constructed in the literatures. However, for all the existing \({\textbf {(1}}+\varvec{\epsilon } {\textbf {)}}\) -optimal MDS codes with the number of helper nodes \({\textbf {d}}\) smaller than \({\textbf {n}}-{\textbf {1}}\) , a few compulsory nodes need to be contacted when repairing a failed node. In this paper, we provide two explicit \({\textbf {(1}}+\varvec{\epsilon } {\textbf {)}}\) -optimal MDS codes contacting any set of \({\textbf {d}}\) helper nodes with \({\textbf {d}}\) smaller than \({\textbf {n}}-{\textbf {1}}\) for the first time.
