Information on Result #548652
There is no linear OA(941, 77, F9, 36) (dual of [77, 36, 37]-code), because construction Y1 would yield
- linear OA(940, 45, F9, 36) (dual of [45, 5, 37]-code), but
- construction Y1 [i] would yield
- OA(939, 41, S9, 36), but
- the (dual) Plotkin bound shows that M ≥ 739 044147 071729 616580 416051 031916 488005 / 37 > 939 [i]
- OA(95, 45, S9, 4), but
- discarding factors would yield OA(95, 44, S9, 4), but
- the Rao or (dual) Hamming bound shows that M ≥ 60897 > 95 [i]
- discarding factors would yield OA(95, 44, S9, 4), but
- OA(939, 41, S9, 36), but
- construction Y1 [i] would yield
- linear OA(936, 77, F9, 32) (dual of [77, 41, 33]-code), but
- discarding factors / shortening the dual code would yield linear OA(936, 50, F9, 32) (dual of [50, 14, 33]-code), but
- construction Y1 [i] would yield
- linear OA(935, 38, F9, 32) (dual of [38, 3, 33]-code), but
- “Mas†bound on codes from Brouwer’s database [i]
- linear OA(914, 50, F9, 12) (dual of [50, 36, 13]-code), but
- discarding factors / shortening the dual code would yield linear OA(914, 44, F9, 12) (dual of [44, 30, 13]-code), but
- construction Y1 [i] would yield
- linear OA(913, 17, F9, 12) (dual of [17, 4, 13]-code), but
- “MPa†bound on codes from Brouwer’s database [i]
- linear OA(930, 44, F9, 27) (dual of [44, 14, 28]-code), but
- discarding factors / shortening the dual code would yield linear OA(930, 39, F9, 27) (dual of [39, 9, 28]-code), but
- residual code [i] would yield OA(93, 11, S9, 3), but
- discarding factors / shortening the dual code would yield linear OA(930, 39, F9, 27) (dual of [39, 9, 28]-code), but
- linear OA(913, 17, F9, 12) (dual of [17, 4, 13]-code), but
- construction Y1 [i] would yield
- discarding factors / shortening the dual code would yield linear OA(914, 44, F9, 12) (dual of [44, 30, 13]-code), but
- linear OA(935, 38, F9, 32) (dual of [38, 3, 33]-code), but
- construction Y1 [i] would yield
- discarding factors / shortening the dual code would yield linear OA(936, 50, F9, 32) (dual of [50, 14, 33]-code), 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 OA(942, 78, F9, 37) (dual of [78, 36, 38]-code) | [i] | Truncation | |
| 2 | No linear OA(943, 79, F9, 38) (dual of [79, 36, 39]-code) | [i] | ||
| 3 | No linear OA(945, 81, F9, 40) (dual of [81, 36, 41]-code) | [i] | ||
| 4 | No linear OOA(942, 77, F9, 2, 37) (dual of [(77, 2), 112, 38]-NRT-code) | [i] | m-Reduction for OOAs | |
| 5 | No linear OOA(943, 77, F9, 2, 38) (dual of [(77, 2), 111, 39]-NRT-code) | [i] | ||
| 6 | No linear OOA(944, 77, F9, 2, 39) (dual of [(77, 2), 110, 40]-NRT-code) | [i] | ||
| 7 | No linear OOA(945, 77, F9, 2, 40) (dual of [(77, 2), 109, 41]-NRT-code) | [i] | ||
| 8 | No linear OOA(946, 77, F9, 2, 41) (dual of [(77, 2), 108, 42]-NRT-code) | [i] | ||
| 9 | No linear OOA(941, 77, F9, 2, 36) (dual of [(77, 2), 113, 37]-NRT-code) | [i] | Depth Reduction | |
| 10 | No linear OOA(941, 77, F9, 3, 36) (dual of [(77, 3), 190, 37]-NRT-code) | [i] | ||
| 11 | No digital (5, 41, 77)-net over F9 | [i] | Extracting Embedded Orthogonal Array | |