Information on Result #1856885
There is no (34, 115)-sequence in base 4, because net from sequence would yield (34, m, 116)-net in base 4 for arbitrarily large m, but
- m-reduction [i] would yield (34, 459, 116)-net in base 4, but
- extracting embedded OOA [i] would yield OOA(4459, 116, S4, 4, 425), but
- the (dual) Plotkin bound for OOAs shows that M ≥ 194 992852 130599 185118 421166 892634 703653 381612 518469 560737 770682 006780 472144 656754 839382 785075 398920 255753 826638 366254 610478 883239 042686 972447 623448 278025 876088 293543 397451 145808 333760 597434 939212 472810 192178 080192 407908 866115 292083 856202 225015 583502 210766 031265 206134 808795 676672 / 71 > 4459 [i]
- extracting embedded OOA [i] would yield OOA(4459, 116, S4, 4, 425), 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 (34, 115)-sequence in base 4 (for arbitrarily large k) | [i] | Logical Equivalence (for Sequences) | |
| 2 | No (34, m, 115)-net in base 4 with m > ∞ | [i] | ||
| 3 | No digital (34, 115)-sequence over F4 (for arbitrarily large k) | [i] | ||
| 4 | No digital (34, m, 115)-net over F4 with m > ∞ | [i] | ||