Information on Result #548584
There is no linear OA(333, 67, F3, 21) (dual of [67, 34, 22]-code), because construction Y1 would yield
- linear OA(332, 45, F3, 21) (dual of [45, 13, 22]-code), but
- construction Y1 [i] would yield
- linear OA(331, 37, F3, 21) (dual of [37, 6, 22]-code), but
- “Bou†bound on codes from Brouwer’s database [i]
- OA(313, 45, S3, 8), but
- discarding factors would yield OA(313, 41, S3, 8), but
- the Rao or (dual) Hamming bound shows that M ≥ 1 708963 > 313 [i]
- discarding factors would yield OA(313, 41, S3, 8), but
- linear OA(331, 37, F3, 21) (dual of [37, 6, 22]-code), but
- construction Y1 [i] would yield
- OA(334, 67, S3, 22), but
- discarding factors would yield OA(334, 64, S3, 22), but
- the linear programming bound shows that M ≥ 14 111105 234476 582146 780186 612485 543683 142605 088372 524627 579947 507340 583313 / 837 608500 983525 185318 819414 283441 298949 343873 086193 807233 > 334 [i]
- discarding factors would yield OA(334, 64, S3, 22), but
Mode: Bound (linear).
Optimality
Show details for fixed k and m, n and k, k and s, k and t, n and m, m and s, m and t, n and s, n and t.
Compare with Markus Grassl’s online database of code parameters.
Other Results with Identical Parameters
None.
Depending Results
The following results depend on this result:
| Result | This result only | Method | ||
|---|---|---|---|---|
| 1 | No linear OOA(333, 67, F3, 2, 21) (dual of [(67, 2), 101, 22]-NRT-code) | [i] | Depth Reduction | |
| 2 | No linear OOA(333, 67, F3, 3, 21) (dual of [(67, 3), 168, 22]-NRT-code) | [i] | ||
| 3 | No linear OOA(333, 67, F3, 4, 21) (dual of [(67, 4), 235, 22]-NRT-code) | [i] | ||
| 4 | No linear OOA(333, 67, F3, 5, 21) (dual of [(67, 5), 302, 22]-NRT-code) | [i] | ||
| 5 | No digital (12, 33, 67)-net over F3 | [i] | Extracting Embedded Orthogonal Array | |