In this paper, a new construction of interference-free zero correlation zone (IF-ZCZ) sequence sets is proposed by well designed finite Zak transform lattice tessellation. Each set is characterized by the period of sequences $KM^2$, the set size $K$ and the length of zero correlation zone $M^2-1$, which is optimal with respect to the Tang-Fan-Matsufuji bound. In particular, all sequences in these sets have sparse and highly structured Zak and Fourier spectra, which can decrease the computational complexity of the implementation of the banks of matched filters. Moreover, for the parameters proposed in this paper, the new construction is essentially different from the general construction of optimal IF-ZCZ sequence sets given by Popovic.
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