Information on Result #1850460
There is no (115, m, 244)-net in base 3 for arbitrarily large m, because m-reduction would yield (115, 1457, 244)-net in base 3, but
- extracting embedded OOA [i] would yield OOA(31457, 244, S3, 6, 1342), but
- the (dual) Plotkin bound for OOAs shows that M ≥ 266 672401 743753 848206 673293 072843 136219 212257 063515 913347 357755 534533 071260 071766 072393 957455 776916 183767 084366 593059 551011 220358 595677 122915 781750 923767 211039 127644 120910 800400 319611 496541 239277 781683 438007 480763 347427 365977 446505 440962 323991 146432 367451 174299 842321 063715 427970 789046 261702 918629 924561 122260 854310 923915 371097 970417 736264 457197 668107 806195 947946 543857 582279 751640 520341 948770 826205 178634 594453 112412 906424 308428 646735 568820 778149 119724 702922 492287 938422 050234 087169 333359 949856 975758 691659 495067 185762 158959 350397 431664 502401 605391 150181 333268 927339 350613 463734 397017 268718 594605 265614 013579 416557 293538 277790 048722 096443 882298 363282 230002 054950 349759 888670 432618 416695 545121 123223 / 1343 > 31457 [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 (115, 243)-sequence in base 3 | [i] | Net from Sequence | |
| 2 | No (115, 115+k, 244)-net in base 3 for arbitrarily large k | [i] | Logical Equivalence (for Nets with Unbounded m) | |
| 3 | No (115, m, 244)-net in base 3 with unbounded m | [i] | ||
| 4 | No digital (115, 115+k, 244)-net over F3 for arbitrarily large k | [i] | ||
| 5 | No digital (115, m, 244)-net over F3 with unbounded m | [i] | ||