Looking for good Hofmeister and Braunschadel bases

TL;DR

This paper explores the search for extremal Hofmeister and Braunschadel bases related to the Postage Stamp Problem, including early attempts and unpublished correspondence, to identify bases that maximize coverage for large parameters.

Contribution

It presents initial efforts and unpublished correspondence on identifying extremal bases for large parameters in the Postage Stamp Problem.

Findings

Early methods for finding extremal bases are described.

Unpublished correspondence provides additional insights.

Progress towards large parameter bases is documented.

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 "global" Postage Stamp Problem. This paper describes the author's early attempts to identify extremal Hofmeister and Braunschadel bases for large t (where t = 12h + r for some 0 <= r <= 11), and also includes a transcription of Prof. Selmer's correspondence with the author about this work which has not been published before. See (Selmer, E.S., Private Communication, [8], 1992/1993).