Hypercubic 4 and 5-designs from double-error-correcting BCH codes

Abstract:

An ordered orthogonal array OOA(τ,k,n) is a binary 2^{k} × nτ matrix with the property that for each complete τ-set of columns, each possible τ-tuple occurs in exactly 2^{k-τ} rows of those columns (for definition of a complete τ-set, see in the paper). OOA(τ,k,n) give uniformly distributed sets of points in continuous unit cube. The best known constructions of OOA(τ,k,n) for τ=4 and τ=5 are given which are obtained with the help of BCH codes.