Information on Result #599595
There is no digital (61, 233, 288)-net over F4, because extracting embedded orthogonal array would yield linear OA(4233, 288, F4, 172) (dual of [288, 55, 173]-code), but
- residual code [i] would yield OA(461, 115, S4, 43), but
- the linear programming bound shows that M ≥ 8 867577 820394 892078 302903 376011 219649 893047 268294 051459 959774 715216 956970 670840 325873 158120 379501 398960 032970 458008 737468 823847 270763 370822 590292 322808 758272 / 1 568698 363933 661749 730985 011129 979312 182529 988673 402786 941022 163461 443141 672915 973490 090934 276533 827022 911521 994930 215625 > 461 [i]
Mode: Bound (linear).
Optimality
Show details for fixed k and m, k and s, k and t, 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 digital (61, 234, 288)-net over F4 | [i] | m-Reduction | |
| 2 | No digital (61, 235, 288)-net over F4 | [i] | ||
| 3 | No digital (61, 236, 288)-net over F4 | [i] | ||