Information on Result #1852080
There is no (36, m, 237)-net in base 7 for arbitrarily large m, because m-reduction would yield (36, 707, 237)-net in base 7, but
- extracting embedded OOA [i] would yield OOA(7707, 237, S7, 3, 671), but
- the (dual) Plotkin bound for OOAs shows that M ≥ 33551 116362 679030 638211 754453 352241 648893 587517 129324 668148 409592 402660 039400 705621 134716 379072 903557 074025 996955 696978 800825 650234 648040 180201 043726 181323 052337 727612 545302 496869 602040 919324 524723 626201 950079 963738 941308 253244 468536 870244 907499 384147 098822 526314 104536 294412 801990 185079 045469 466915 704001 670137 699992 875984 853355 475590 610245 044571 001862 445533 145615 698447 182871 778055 011502 118206 031910 040763 590803 068548 716052 181107 863804 091938 608302 833633 480064 526678 995539 786724 159532 002888 088495 999010 864557 861229 880340 673008 126550 155808 489684 350821 866424 366243 523284 604878 839484 634516 928185 718973 / 8 > 7707 [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 (36, 236)-sequence in base 7 | [i] | Net from Sequence | |
| 2 | No (36, 36+k, 237)-net in base 7 for arbitrarily large k | [i] | Logical Equivalence (for Nets with Unbounded m) | |
| 3 | No (36, m, 237)-net in base 7 with unbounded m | [i] | ||
| 4 | No digital (36, 36+k, 237)-net over F7 for arbitrarily large k | [i] | ||
| 5 | No digital (36, m, 237)-net over F7 with unbounded m | [i] | ||