A new design method for families of sequences with large linear span

low cross correlation and large sequences number is presented.The key idea of the new design is to use the analytical method of shift sequences to improve phase-controlled sequences in theory and use interleaved sequences to be basic sequences instead of the original sequences with the two-level autocorrelation function to construct a set of long sequences with the desire properties.The correlation property has also been analyzed

and the maximal correlation value is optimal with respect to the Welch bound.The linear span

the number of families and the number of sequences in each family of the new sequence families are all larger than that of any other sequence families

and some new sequences are balanced.