Notes on "Symmetric Bases with large 2-range"

TL;DR

This paper explores symmetric bases with large 2-range, presenting new computational findings of extremal bases that surpass previous results and offering an improved theoretical insight into the Postage Stamp Problem.

Contribution

It provides new computational data on extremal symmetric bases and enhances existing theoretical results related to the Postage Stamp Problem.

Findings

Discovered new extremal bases surpassing previous records

Improved theoretical bounds for symmetric bases

Extended the known range of bases for k<=75

Abstract

A_k = {1, a_2, ... a_k} is an h-basis for n if every positive integer not exceeding n can be expressed as the sum of no more than h values a_i. An extremal h-basis A_k is one for which n is as large as possible. Computing extremal bases has become known as the Postage Stamp Problem. This paper is inspired by and based upon a paper entitled "Symmetric bases with large 2-range for k<=75" by Svein Mossige at the University of Bergen (Mossige, Svein, [4]). Computer searches have identified some further bases which are superior to those reported in [4], and the paper also reports an improvement to one of the theoretical results.