Power-sequence terraces for [formula omitted] where n is an odd prime power

Abstract

A power-sequence terrace for Z n is defined to be a terrace which can be partitioned into segments one of which contains merely the zero element of Z n , whilst each other segment is either (a) a sequence of successive powers of an element of Z n , or (b) such a sequence multiplied throughout by a constant. Many elegant families of such Z n terraces are constructed for values of n that are odd prime powers. The discovery of these families greatly increases the number of known constructions for terraces for Z n . Tables are provided to show clearly the constructions available for each prime power n satisfying n<300.