Zero correlation zone (ZCZ) sequence sets are aimed for possible applications in the quasi-synchronous code-division multiple access (QS-CDMA) communication systems. In this paper, we first discuss the relationship between the upper bound on the zone length and the upper bound on the set size, which are both derived from the bound given by Tang, Fan and Matsufuji. Next, we show that several known constructions can achieve the upper bound of zone length.