As a special case of sparse code multiple access (SCMA), low-density signatures based code-division multiple access (LDS-CDMA) was widely believed to have worse error rate performance compared to SCMA. With the aid of Eisenstein numbers, we present a novel class of LDS which can achieve error rate performances comparable to that of SCMA in Rayleigh fading channels and better performances in Gaussian channels. This is achieved by designing power-imbalanced LDS such that variation of user powers can be seen both in every chip window and the entire sequence window. As LDS-CDMA is more flexible in terms of its backwards compatibility, our proposed LDS are a promising sequence candidate for dynamic machine-type networks serving a wide range of communication devices.