New explicit bounds for ordered codes and (t,m,s)(t,m,s)-nets

We derive two explicit bounds from the linear programming bound for ordered codes and ordered orthogonal arrays. While ordered codes generalize the concept of error-correcting block codes in Hamming space, ordered orthogonal arrays play an important role in the context of numerical integration and quasi-Monte Carlo methods because of their equivalence to (t,m,s)(t,m,s)-nets, low-discrepancy point sets in the ss-dimensional unit cube whenever tt is reasonably small. The first bound we prove is a refinement of the Plotkin bound; the second bound shares its parameter range with the quadratic bound by Bierbrauer as well as the Plotkin bound. Both bounds yield improvements for various parameters.