This work describes an M² × M Zak space construction of new zero correlation zone polyphase sequence sets, of sequence length M³ and set size M, with all-zero cross-correlation. The construction includes the sets with (M-1)-point, (T₂M-1)-point and (M² -1)-point zero auto correlation zone, where T₂ is an arbitrary non-trivial factor of M. All sequences in these sets have sparse discrete Fourier transforms with constant non-zero magnitude at M² points and zero magnitude at (M -1)M² points.