  In the literature, there are several well-known periodic channel hopping (CH)
sequences that can achieve maximum rendezvous diversity in a cognitive radio
network (CRN). For a CRN with $N$ channels, it is known that the period of such
a CH sequence is at least $N^2$. The asymptotic approximation ratio, defined as
the ratio of the period of a CH sequence to the lower bound $N^2$ when $N \to
\infty$, is still 2.5 for the best known CH sequence in the literature. An open
question in the multichannel rendezvous problem is whether it is possible to
construct a periodic CH sequence that has the asymptotic approximation ratio 1.
In this paper, we tighten the theoretical gap by proposing CH sequences, called
IDEAL-CH, that have the asymptotic approximation ratio 2.
  For a weaker requirement that only needs the two users to rendezvous on one
commonly available channel in a period, we propose channel hopping sequences,
called ORTHO-CH, with period $(2p +1)p$, where $p$ is the smallest prime not
less than $N$.
