In DS-CDMA systems and DS-UWB radios, low correlation of spreading sequences can greatly help to minimize multiple access interference (MAI) and large linear span of spreading sequences can reduce their predictability. In this letter, new sequence sets with low correlation and large linear span are proposed. Based on the construction Tr^m₁[Trⁿ_m(α^bt+γ_iα^dt)]^r for generating p-ary sequences of period pⁿ-1, where n=2m, d=up^m±v, b=u±v, γ_i∈GF(pⁿ), and p is an arbitrary prime number, several methods to choose the parameter d are provided. The obtained sequences with family size pⁿ are of four-valued, five-valued, six-valued or seven-valued correlation and the maximum nontrivial correlation value is (u+v-1)p^m-1. The simulation by a computer shows that the linear span of the new sequences is larger than that of the sequences with Niho-type and Welch-type decimations, and similar to that of [10].