Information on Result #1857453
There is no (39, 296)-sequence in base 8, because net from sequence would yield (39, m, 297)-net in base 8 for arbitrarily large m, but
- m-reduction [i] would yield (39, 887, 297)-net in base 8, but
- extracting embedded OOA [i] would yield OOA(8887, 297, S8, 3, 848), but
- the (dual) Plotkin bound for OOAs shows that M ≥ 518513 968422 523323 510504 843469 278219 267631 552966 925948 010799 160945 476315 889909 493675 376543 944633 472682 378271 336649 236117 661987 428536 571067 221392 199562 425346 710025 692207 219581 302032 881643 311825 554972 423545 001287 571783 836784 489786 005980 474710 896841 102485 133250 882033 589582 048894 906468 771247 769786 160528 632008 002647 317992 130060 801958 896797 487235 603585 520380 478603 627793 480636 792085 498638 170479 956378 035980 113262 898405 249819 007349 288140 093139 162502 232172 435635 193977 782087 229335 232750 180314 194809 735495 715280 468660 479062 695091 283230 674068 954892 027126 877562 502784 256355 598771 340153 920664 089479 450336 422801 170447 173413 767385 564098 178587 683222 817821 673833 770407 732301 855788 161188 733413 833972 684760 471500 112935 803572 217180 409077 145809 643547 633467 920979 713632 286478 317939 317278 457156 730905 050962 423508 835546 169344 / 283 > 8887 [i]
- extracting embedded OOA [i] would yield OOA(8887, 297, S8, 3, 848), 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 (39, 296)-sequence in base 8 (for arbitrarily large k) | [i] | Logical Equivalence (for Sequences) | |
| 2 | No (39, m, 296)-net in base 8 with m > ∞ | [i] | ||
| 3 | No digital (39, 296)-sequence over F8 (for arbitrarily large k) | [i] | ||
| 4 | No digital (39, m, 296)-net over F8 with m > ∞ | [i] | ||