Information on Result #1878902
There is no digital (41, 41+k, 138)-net over F4 for arbitrarily large k, because logical equivalence would yield (41, m, 138)-net in base 4 for arbitrarily large m, but
- m-reduction [i] would yield (41, 547, 138)-net in base 4, but
- extracting embedded OOA [i] would yield OOA(4547, 138, S4, 4, 506), but
- the (dual) Plotkin bound for OOAs shows that M ≥ 59 425560 645910 630905 884124 990717 921563 902855 803263 824051 497735 550591 822807 998080 881523 590364 033077 591306 279900 423082 302703 294424 251652 818623 805523 999752 750658 250215 309902 957701 550030 630720 478197 104912 577302 226397 243493 156503 068559 920929 376390 888476 665893 948828 900870 559790 117517 802383 038493 146955 037678 505795 160026 650958 668255 723520 / 169 > 4547 [i]
- extracting embedded OOA [i] would yield OOA(4547, 138, S4, 4, 506), 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.