Information on Result #1856594
There is no (255, 266)-sequence in base 2, because net from sequence would yield (255, m, 267)-net in base 2 for arbitrarily large m, but
- m-reduction [i] would yield (255, 2125, 267)-net in base 2, but
- extracting embedded OOA [i] would yield OOA(22125, 267, S2, 8, 1870), but
- the (dual) Plotkin bound for OOAs shows that M ≥ 9 571871 447801 398635 452438 419123 227434 408663 534486 519833 184391 405456 200473 800183 258050 856815 836164 089414 467855 501841 071407 282046 650274 684640 537725 098549 449214 484260 004610 445844 892815 596686 729212 939584 600667 405853 206712 786703 709130 904061 288523 078322 818764 021726 153242 438186 750596 647210 546213 288756 918802 942710 090288 820722 467756 140344 477066 784477 787024 528960 873659 931009 752404 801897 695994 262427 434743 216038 342064 599342 011690 724920 697226 930497 515302 052980 882584 081473 563111 776543 559956 447741 069620 275628 297667 015190 394592 950522 626740 458825 418791 704177 571118 299103 187207 621934 993535 613724 618077 586683 290604 917763 681893 071932 805317 661885 551314 206720 / 1871 > 22125 [i]
- extracting embedded OOA [i] would yield OOA(22125, 267, S2, 8, 1870), 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 (255, 266)-sequence in base 2 (for arbitrarily large k) | [i] | Logical Equivalence (for Sequences) | |
| 2 | No (255, m, 266)-net in base 2 with m > ∞ | [i] | ||
| 3 | No digital (255, 266)-sequence over F2 (for arbitrarily large k) | [i] | ||
| 4 | No digital (255, m, 266)-net over F2 with m > ∞ | [i] | ||