On the local base of a primitive and nonpowerful sign pattern

Denote by l A ( k ) the k th smallest local base of a primitive and nonpowerful sign pattern A . In this paper, more "gaps" for the k th local base are shown, and the primitive and nonpowerful sign patterns with the k th local base in 2 n 2 - 8 n + 9 + k , 2 n 2 - 4 n + k ] are completely characterized.