Information on Result #1856932
There is no (81, 258)-sequence in base 4, because net from sequence would yield (81, m, 259)-net in base 4 for arbitrarily large m, but
- m-reduction [i] would yield (81, 1031, 259)-net in base 4, but
- extracting embedded OOA [i] would yield OOA(41031, 259, S4, 4, 950), but
- the (dual) Plotkin bound for OOAs shows that M ≥ 180023 821340 602244 829070 263486 837287 592771 500567 810286 730024 017024 751742 930371 918294 008602 294973 080824 285824 724393 088231 473162 651421 358705 415454 258157 853348 020461 540227 192236 788859 981580 410580 440033 846838 076751 433139 967661 481831 908884 888814 798141 816176 603293 117519 359419 707814 758382 999550 796887 092463 801648 372955 109007 150881 554970 893147 045128 245266 019975 347396 603845 901093 643041 268054 040687 592864 507065 470479 348872 401129 914884 121943 070994 965456 609235 061776 372820 518784 577254 222706 627486 571144 595974 553267 252502 158102 975249 049830 543196 480094 097875 870882 344043 885768 311558 931506 453025 304177 602238 641094 495891 624144 378643 087360 / 317 > 41031 [i]
- extracting embedded OOA [i] would yield OOA(41031, 259, S4, 4, 950), but
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 (81, 258)-sequence in base 4 (for arbitrarily large k) | [i] | Logical Equivalence (for Sequences) | |
| 2 | No (81, m, 258)-net in base 4 with m > ∞ | [i] | ||
| 3 | No digital (81, 258)-sequence over F4 (for arbitrarily large k) | [i] | ||
| 4 | No digital (81, m, 258)-net over F4 with m > ∞ | [i] | ||