Information on Result #1850394
There is no (93, m, 200)-net in base 3 for arbitrarily large m, because m-reduction would yield (93, 993, 200)-net in base 3, but
- extracting embedded OOA [i] would yield OOA(3993, 200, S3, 5, 900), but
- the (dual) Plotkin bound for OOAs shows that M ≥ 778 008753 850845 057923 189720 759492 363510 515846 434391 720066 187706 405088 433829 542389 441692 587986 160299 838844 025558 241890 028399 121420 742339 524266 436253 958384 260847 529597 544690 843434 387295 122394 947745 834679 904589 186748 483290 278329 639936 801662 398134 709442 189886 351736 393782 921782 834480 561983 958426 122059 477397 035303 409072 511675 997953 347921 637975 182137 257472 362718 304848 314294 776024 812638 820818 507809 500016 870763 954447 831340 566118 117086 852459 962323 925833 406808 053089 521382 523079 409301 / 901 > 3993 [i]
Mode: Bound.
Optimality
Show details for fixed m and s, m and t, t and s.
Other Results with Identical Parameters
None.
Depending Results
The following results depend on this result:
| Result | This result only | Method | ||
|---|---|---|---|---|
| 1 | No (93, 199)-sequence in base 3 | [i] | Net from Sequence | |
| 2 | No (93, 93+k, 200)-net in base 3 for arbitrarily large k | [i] | Logical Equivalence (for Nets with Unbounded m) | |
| 3 | No (93, m, 200)-net in base 3 with unbounded m | [i] | ||
| 4 | No digital (93, 93+k, 200)-net over F3 for arbitrarily large k | [i] | ||
| 5 | No digital (93, m, 200)-net over F3 with unbounded m | [i] | ||