Information on Result #1850628
There is no (171, m, 357)-net in base 3 for arbitrarily large m, because m-reduction would yield (171, 1778, 357)-net in base 3, but
- extracting embedded OOA [i] would yield OOA(31778, 357, S3, 5, 1607), but
- the (dual) Plotkin bound for OOAs shows that M ≥ 58505 284399 621133 028236 078689 494643 076501 679493 374004 681109 828449 757531 969411 318469 899269 733131 311817 564005 399267 829402 246818 999308 718101 684029 476004 498731 111390 276841 688929 697395 200427 820078 779058 254071 201828 516868 514073 379765 478819 406444 555254 120242 130215 809479 708473 035981 312861 389561 843043 928453 879895 684426 056017 974092 989469 946724 984206 351491 020674 386244 614951 464857 190694 161071 368611 232635 718828 703173 572165 507593 363460 718953 492480 944418 066060 752311 085858 884304 526633 708194 325029 675501 927283 627361 133929 253336 255161 650195 330070 575160 892068 233339 376642 162023 761199 339007 263863 219094 900624 331852 955538 749548 490945 453678 060840 759031 365006 405454 147261 771619 411920 233918 564493 049317 171411 466324 714824 751778 617787 884842 623494 177456 471673 388514 201889 488810 266540 257450 464411 637733 626875 965328 980516 911467 129171 122826 461230 635927 506250 806527 499864 719631 / 268 > 31778 [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 (171, 356)-sequence in base 3 | [i] | Net from Sequence | |
| 2 | No (171, 171+k, 357)-net in base 3 for arbitrarily large k | [i] | Logical Equivalence (for Nets with Unbounded m) | |
| 3 | No (171, m, 357)-net in base 3 with unbounded m | [i] | ||
| 4 | No digital (171, 171+k, 357)-net over F3 for arbitrarily large k | [i] | ||
| 5 | No digital (171, m, 357)-net over F3 with unbounded m | [i] | ||