  Sequences with low/zero ambiguity zone (LAZ/ZAZ) properties are useful for
modern wireless communication and radar systems operating in mobile
environments. This paper first presents a new family of ZAZ sequence sets by
generalizing an earlier construction of zero correlation zone (ZCZ) sequences
arising from perfect nonlinear functions. We then introduce a second family of
ZAZ sequence sets with comb-like spectrum, whereby the local Doppler resilience
is ensured by their inherent spectral nulls in the frequency-domain. Finally,
LAZ sequence sets are obtained thanks to its connection with a novel class of
mapping functions. These proposed unimodular ZAZ and LAZ sets are cyclically
distinct and asymptotically optimal with respect to the existing theoretical
bounds.
