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Given an integral \stamp" basis Ak with 1 = a1 <a 2 <: :: < a k and a positive integer h, we dene the h-range n(h;Ak )a s n (h;Ak )=m ax f N 2 N j n N = ) n = k X 1 x i a i ; k X 1 x ih; n; xi 2 N0g: We give an algorithm to determine the h-range. We prove some properties of the h-range formula, and we conjecture its form for the extremal h-range. We consider parameter bases Ak = Ak(h), where the basis elements ai are given functions of h .F or k= 4 we conjecture the extremal parameter bases for h 11385.

The Postage Stamp Problem: An algorithm to determine the $h$-range on the $h$-range formula on the extremal basis problem for $k=4$