Information on Result #1850739
There is no (208, m, 431)-net in base 3 for arbitrarily large m, because m-reduction would yield (208, 2579, 431)-net in base 3, but
- extracting embedded OOA [i] would yield OOA(32579, 431, S3, 6, 2371), but
- the (dual) Plotkin bound for OOAs shows that M ≥ 4123 838956 759161 040260 921133 800680 799013 928830 416796 720894 120572 258159 116264 533448 569568 359070 854587 362741 989867 738620 757174 526277 808918 036207 325808 108084 124895 319250 258493 939568 426551 089500 042636 293084 306654 387991 148964 569700 280602 159532 101388 988094 350711 807654 468557 783683 430631 556969 222804 370550 124262 481032 501914 719797 882884 943987 497473 621159 950758 805259 782836 961348 104314 233711 646669 388750 828644 871972 375998 331611 413647 425914 244978 300413 991077 693244 593570 846648 386092 581134 453045 235175 661694 189888 264412 296078 397543 361933 765511 224754 470182 128616 108584 668288 069217 376920 057784 356875 969055 641970 307970 193041 527414 087267 030420 718213 413723 446841 270114 706623 550516 278639 976839 801405 179738 346222 507950 445001 412120 566571 302838 074755 246072 145627 723115 363229 892154 390569 912165 192310 852965 331456 928938 680223 684839 174794 550910 749015 084667 446405 684233 082840 437276 038140 679452 949455 843485 173099 091732 876288 859765 089598 501988 529521 064061 499383 827270 295988 939620 034866 060430 961113 100757 017999 999359 302507 867071 590124 234093 689300 906321 613915 314458 860592 178440 183085 869965 097025 463709 444872 015960 530200 781804 444159 785007 347155 753592 530625 062217 929922 273942 412729 199826 659982 478097 062090 490828 208550 049528 250897 226084 261709 386672 358085 760641 596839 / 1186 > 32579 [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 (208, 430)-sequence in base 3 | [i] | Net from Sequence | |
| 2 | No (208, 208+k, 431)-net in base 3 for arbitrarily large k | [i] | Logical Equivalence (for Nets with Unbounded m) | |
| 3 | No (208, m, 431)-net in base 3 with unbounded m | [i] | ||
| 4 | No digital (208, 208+k, 431)-net over F3 for arbitrarily large k | [i] | ||
| 5 | No digital (208, m, 431)-net over F3 with unbounded m | [i] | ||