Information on Result #1856902
There is no (51, 167)-sequence in base 4, because net from sequence would yield (51, m, 168)-net in base 4 for arbitrarily large m, but
- m-reduction [i] would yield (51, 667, 168)-net in base 4, but
- extracting embedded OOA [i] would yield OOA(4667, 168, S4, 4, 616), but
- the (dual) Plotkin bound for OOAs shows that M ≥ 299 988221 142963 048588 365030 287739 055137 477589 689678 807886 832557 189121 871400 795355 850504 138804 433447 020182 196579 639140 992166 812281 808357 066856 866067 889596 292531 465534 215458 073816 035764 104743 037391 715672 186116 745874 943494 059101 730649 588018 080539 118538 030742 753976 108019 321311 153470 937823 467021 428485 814382 438412 807737 387188 203377 916682 155833 446632 290887 317107 963196 767235 375584 261873 850141 325130 420400 947200 / 617 > 4667 [i]
- extracting embedded OOA [i] would yield OOA(4667, 168, S4, 4, 616), but
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 (51, 167)-sequence in base 4 (for arbitrarily large k) | [i] | Logical Equivalence (for Sequences) | |
| 2 | No (51, m, 167)-net in base 4 with m > ∞ | [i] | ||
| 3 | No digital (51, 167)-sequence over F4 (for arbitrarily large k) | [i] | ||
| 4 | No digital (51, m, 167)-net over F4 with m > ∞ | [i] | ||