## NRT-Code Embedding in Larger Space

Every (linear) ordered orthogonal array OOA(bm, s, Sb, T , k) yields a (linear) OOA(bm+T, s + 1, Sb, T , k). Correspondingly, every (linear) ((s, T ), N, d)-NRT-code yields a (linear) ((s + 1, T ), N, d)-code over the same field.

Note that there is no corresponding propagation rule for nets, because mʹ = b + T turns towards infinity if T →∞.

### Construction for OOAs

Based on a given OOA A the new orthogonal array Aʹ is obtained as

Aʹ = {(x,y)  :  xA,ySbT }.

If H is a generator matrix of A, the generator matrix of Aʹ is given by

Hʹ = .

In other words, Aʹ is the direct product of A and the complete OOA OOA(bT , 1, Sb, T , T ).

### Construction for Linear NRT-Codes

The new linear NRT-code Cʹ is obtained by embedding CFb(s,T ) in Fb(s+1,T ). In other words, Cʹ is constructed by appending a 0-block to every code word of C or by appending an all-zero block to the generator matrix of C.