## Generalized (Dual) Plotkin Bound for OOAs

In [1, Theorem 2] the Plotkin bound for linear codes is generalized to NRT space. Using duality theory [2] the following bound for linear ordered orthogonal arrays is obtained: For every linear OOA(bm, s, Sb, T , k) we have

(bTs−m – 1) ≤ bTs−mρT

with

ρT = T = T .

It is easy to see that the original Plotkin bound is obtained for T = 1.

In [3, Theorem 5] and [4, Theorem 6] this bound is derived for arbitrary (not necessarily linear) OOAs from the linear programming bound for OOAs.

### Application to Nets and Sequences

In [5, Chapter 3] and [6] Schürer uses the dual Plotkin bound for OOAs for deriving the following bound for (t, s)-sequences: Let tb(s) be the minimum t such that a (t, s)-sequence in base b can exist. Then

tb(s) ≥  sO(log s)

and therefore

.

The bound 1/(b−1) is the best result for digital as well as arbitrary (t, s)-sequences known today.