An (n, d, a, b)-perfect array is a d-dimensional b1×b2×...×bd sized n-ary periodic array containing all possible a1×a2×...×ad sized n-ary array exactly once as subarray. If a1=a2=...=ad and term double cube are used. If d≥4, then the double cube is called double hypercube. We prove the existence of (N, d, a, b)-perfect double cubes for arbitrary d≥1, a≥2 and n≥2, where N=kn with a suitable k≥1. Further we illustrate the main theorem constructing 4 and 5-dimensional hypercubes.
- De Bruijn arrays
- Four- and five-dimensional perfect arrays
- Perfect cubes
ASJC Scopus subject areas
- Discrete Mathematics and Combinatorics
- Applied Mathematics