  Complementary set sequences (CSSs) are useful for dealing with the high
peak-to-average power ratio (PAPR) problem in orthogonal frequency division
multiplexing (OFDM) systems. In practical OFDM transmission, however, certain
sub-carriers maybe reserved and/or prohibited to transmit signals, leading to
the so-called \emph{spectral null constraint} (SNC) design problem. For
example, the DC sub-carrier is reserved to avoid the offsets in D/A and A/D
converter in the LTE systems. While most of the current research focus on the
design of low PAPR CSSs to improve the code-rate, few works address the
aforementioned SNC in their designs. This motivates us to investigate CSSs with
SNC as well as low PAPR property. In this paper, we present systematic
constructions of CSSs under SNCs and low PAPR. First, we show that mutually
orthogonal complementary sets (MOCSs) can be used as \emph{seed sequences} to
generate new CSSs with SNC and low PAPR, and then provide an iterative
technique for the construction of MOCSs which can be further used to generate
complementary sets (CSs) with low PAPRs and spectral nulls at \emph{varying}
positions in the designed sequences. Next, inspired by a recent idea of Chen,
we propose a novel construction of these \emph{seed} MOCSs with
non-power-of-two lengths from generalized Boolean functions.
