In this correspondence, we devise a new method for constructing a ternary column sequence set of length 3m+1-1 form ternary sequences of period 3m-1 with ideal autocorrelation, and the ternary LCZ sequence set of period 3n-1 is constructed by using the column sequence set when (m+1)|n. In addition, the method is popularized to the p-ary LCZ sequence. The resultant LCZ sequence sets in this paper are optimal with respect to the Tang-Fan-Matsufuji bound.