Information on Result #1858051
There is no (10, 308)-sequence in base 27, because net from sequence would yield (10, m, 309)-net in base 27 for arbitrarily large m, but
- m-reduction [i] would yield (10, 307, 309)-net in base 27, but
- extracting embedded OOA [i] would yield OA(27307, 309, S27, 297), but
- the (dual) Plotkin bound for OOAs shows that M ≥ 4347 009720 687972 361558 417905 994789 140019 544758 728076 851890 809652 712046 478433 017814 958813 290050 657477 356785 611158 442705 778247 089602 353080 274213 057877 310064 805232 113682 767630 062467 517211 266833 202017 197976 049929 203290 028232 267664 965006 872521 371461 129653 545325 086016 456179 936745 972049 595074 009395 156550 125675 460871 098745 545402 649262 043271 795624 985036 008465 167997 908430 681296 249126 855467 119321 220035 054925 920393 354322 569562 642726 587623 705785 646886 / 149 > 27307 [i]
- extracting embedded OOA [i] would yield OA(27307, 309, S27, 297), 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 (10, 308)-sequence in base 27 (for arbitrarily large k) | [i] | Logical Equivalence (for Sequences) | |
| 2 | No (10, m, 308)-net in base 27 with m > ∞ | [i] | ||
| 3 | No digital (10, 308)-sequence over F27 (for arbitrarily large k) | [i] | ||
| 4 | No digital (10, m, 308)-net over F27 with m > ∞ | [i] | ||