An additive 2-basis with range n is restricted if its largest element is n 2. Among the restricted 2-bases of given length k, the ones that have the greatest range are extremal restricted. We describe an algorithm that finds the extremal restricted 2-bases of a given length, and we list them for lengths up to k = 41.
The final ingredient is the gaps test'' by Challis @cite_6 . Based on a simple combinatorial argument, it prunes the search tree of admissible bases, if they are required to have a range of at least a given target value @math . In section we shall prove lower bounds for the ranges of the prefix and the mirrored suffix. With these lower bounds the gaps test prunes the search tree very efficiently.
@cite_6
2017959893
A k = 1, a 2 ,..., a k is an h-basis for n if every positive integer c n can be expressed as the sum of more than h values a i ; an extremal h-basis A k is one for which n is as large as possible. Computing such bases has become known as the Postage Stamp Problem, and this paper describes two new techniques-one appropriate for large k, and the other for large h-which help extend known results in both dimensions. The results themselves are presented as an Appendix