Information on Result #1878408
There is no digital (45, 45+k, 102)-net over F3 for arbitrarily large k, because logical equivalence would yield (45, m, 102)-net in base 3 for arbitrarily large m, but
- m-reduction [i] would yield (45, 504, 102)-net in base 3, but
- extracting embedded OOA [i] would yield OOA(3504, 102, S3, 5, 459), but
- the (dual) Plotkin bound for OOAs shows that M ≥ 424 106443 507026 943329 581755 215793 274192 624762 943282 931142 596161 951220 120634 634556 927691 400379 391590 768506 608050 361286 573501 311585 214440 403491 863714 210779 468698 173939 834894 913202 261998 845703 645281 120294 094227 539678 283489 814188 990573 284443 051664 / 115 > 3504 [i]
- extracting embedded OOA [i] would yield OOA(3504, 102, S3, 5, 459), but
Mode: Bound (linear).
Optimality
Show details for fixed k and s, k and t, t and s.
Other Results with Identical Parameters
None.
Depending Results
None.