AN EQUIVALENCE BETWEEN (T,M,S)-NETS AND STRONGLY ORTHOGONAL HYPERCUBES

It is well known that (t, m, s)-nets are useful in numerical analysis. While many of the best constructions of such nets arise from number t heoretic or algebraic constructions, we will show in this paper that t he existence of a (t, t + k, s)-net in base b is equivalent to the exi stence of a set of s strongly orthogonal hypercubes of dimension t+k, order b and strength k. For k > 2 such generalized orthogonal hypercub es provide new combinatorial structures that may be of interest in var ious other combinatorial settings. (C) 1996 Academic Press, Inc.