Information on Result #1850727
There is no (204, m, 423)-net in base 3 for arbitrarily large m, because m-reduction would yield (204, 2531, 423)-net in base 3, but
- extracting embedded OOA [i] would yield OOA(32531, 423, S3, 6, 2327), but
- the (dual) Plotkin bound for OOAs shows that M ≥ 17311 483451 682111 436420 411817 248705 542219 398441 901094 059948 515309 705399 773866 755518 852734 747526 864639 556355 222193 945352 213107 849496 280402 721178 866563 121418 897791 032754 499209 643674 391078 947867 802612 283903 625437 365003 213595 804073 002511 573315 872881 605784 814945 751372 409772 240839 161502 437906 107076 692935 586298 625020 944912 076526 008180 948047 403572 325606 849278 968966 443531 268338 272727 889862 867329 894314 853923 483370 727237 021076 284199 671735 264299 950940 679697 239961 135622 959753 907371 594102 948945 669155 308818 781154 184508 623251 111972 692413 875313 438840 599350 823590 016669 764865 635657 313371 421485 831582 651128 758226 230313 628284 585630 402928 880449 837996 353838 830021 881620 899951 105213 081967 870317 913537 995595 315578 493073 405338 076866 171856 005017 043827 519008 735349 382047 081466 565170 633648 557774 530343 724681 123389 395588 123007 106074 221870 732302 516127 924058 367288 373930 285892 093038 811946 556880 741715 232450 729475 221313 991542 724536 614918 856087 961251 798377 978909 737872 672885 117804 492290 451380 554034 530613 308896 603016 332683 851795 682332 654822 207615 643639 179177 005222 555541 215350 041576 386401 279322 139779 087901 348757 648427 677928 033498 675978 692185 933549 426963 246583 712932 806169 385392 549196 448773 969062 776174 786787 493390 360564 915200 764568 570627 / 388 > 32531 [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 (204, 422)-sequence in base 3 | [i] | Net from Sequence | |
| 2 | No (204, 204+k, 423)-net in base 3 for arbitrarily large k | [i] | Logical Equivalence (for Nets with Unbounded m) | |
| 3 | No (204, m, 423)-net in base 3 with unbounded m | [i] | ||
| 4 | No digital (204, 204+k, 423)-net over F3 for arbitrarily large k | [i] | ||
| 5 | No digital (204, m, 423)-net over F3 with unbounded m | [i] | ||