Information on Result #1873055
There is no digital (12, m, 18)-net over F2 with m > ∞, because logical equivalence would yield (12, 18)-sequence in base 2, but
- net from sequence [i] would yield (12, m, 19)-net in base 2 for arbitrarily large m, but
- m-reduction [i] would yield (12, 89, 19)-net in base 2, but
- extracting embedded OOA [i] would yield OOA(289, 19, S2, 5, 77), but
- the (dual) Plotkin bound for OOAs shows that M ≥ 9284 550294 640352 061743 431680 / 13 > 289 [i]
- extracting embedded OOA [i] would yield OOA(289, 19, S2, 5, 77), but
- m-reduction [i] would yield (12, 89, 19)-net in base 2, but
Mode: Bound (linear).
Optimality
Show details for fixed t and s.
Other Results with Identical Parameters
None.
Depending Results
None.