Information on Result #1878912
There is no digital (46, 46+k, 153)-net over F4 for arbitrarily large k, because logical equivalence would yield (46, m, 153)-net in base 4 for arbitrarily large m, but
- m-reduction [i] would yield (46, 607, 153)-net in base 4, but
- extracting embedded OOA [i] would yield OOA(4607, 153, S4, 4, 561), but
- the (dual) Plotkin bound for OOAs shows that M ≥ 115 664102 639503 896631 830525 630571 815702 819129 682066 847627 847714 319962 991548 974951 693565 438529 810906 006280 799466 342060 048274 551933 980423 471435 719639 890637 195039 709535 000640 819382 889984 124079 679091 534258 117211 147071 567490 760048 289929 233300 770718 934078 254963 512902 503103 385976 458788 715029 563422 617054 672250 938457 367383 670313 103946 764806 458257 488588 382856 279242 623617 597440 / 281 > 4607 [i]
- extracting embedded OOA [i] would yield OOA(4607, 153, S4, 4, 561), 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.