In this letter, we construct an asynchronous channel hopping sequence set with new parameters based on disjoint relaxed difference sets. Our proposed design attains the shortest maximum-time-to-rendezvous and maximum-first-time-to-rendezvous in asynchronous cognitive radio wireless networks. Moreover, the channel hopping sequences, with varied lengths, can be tailored to diverse scenarios. The innovative construction ensures rendezvous formation among any sequences, featuring uneven and unexpected rendezvous times. This characteristic contributes to memory conservation in small mobile devices over short durations. In fact, the new construction utilizes fewer licensed channels, enhancing both throughput and reliability.