Information on Result #548039
There is no linear OA(1685, 92, F16, 80) (dual of [92, 7, 81]-code), because construction Y1 would yield
- OA(1684, 86, S16, 80), but
- the (dual) Plotkin bound shows that M ≥ 4 479489 484355 608421 114884 561136 888556 243290 994469 299069 799978 201927 583742 360321 890761 754986 543214 231552 / 27 > 1684 [i]
- OA(167, 92, S16, 6), but
- discarding factors would yield OA(167, 80, S16, 6), but
- the Rao or (dual) Hamming bound shows that M ≥ 278 002201 > 167 [i]
- discarding factors would yield OA(167, 80, S16, 6), 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.
Other Results with Identical Parameters
None.
Depending Results
The following results depend on this result:
| Result | This result only | Method | ||
|---|---|---|---|---|
| 1 | No linear OA(1686, 93, F16, 81) (dual of [93, 7, 82]-code) | [i] | Truncation | |
| 2 | No linear OOA(1686, 92, F16, 2, 81) (dual of [(92, 2), 98, 82]-NRT-code) | [i] | m-Reduction for OOAs | |
| 3 | No linear OOA(1687, 92, F16, 2, 82) (dual of [(92, 2), 97, 83]-NRT-code) | [i] | ||
| 4 | No linear OOA(1688, 92, F16, 2, 83) (dual of [(92, 2), 96, 84]-NRT-code) | [i] | ||
| 5 | No linear OOA(1689, 92, F16, 2, 84) (dual of [(92, 2), 95, 85]-NRT-code) | [i] | ||
| 6 | No linear OOA(1690, 92, F16, 2, 85) (dual of [(92, 2), 94, 86]-NRT-code) | [i] | ||
| 7 | No linear OOA(1691, 92, F16, 2, 86) (dual of [(92, 2), 93, 87]-NRT-code) | [i] | ||
| 8 | No linear OOA(1692, 92, F16, 2, 87) (dual of [(92, 2), 92, 88]-NRT-code) | [i] | ||
| 9 | No linear OOA(1693, 92, F16, 2, 88) (dual of [(92, 2), 91, 89]-NRT-code) | [i] | ||
| 10 | No linear OOA(1694, 92, F16, 2, 89) (dual of [(92, 2), 90, 90]-NRT-code) | [i] | ||
| 11 | No linear OOA(1695, 92, F16, 2, 90) (dual of [(92, 2), 89, 91]-NRT-code) | [i] | ||
| 12 | No linear OOA(1696, 92, F16, 2, 91) (dual of [(92, 2), 88, 92]-NRT-code) | [i] | ||
| 13 | No linear OOA(1697, 92, F16, 2, 92) (dual of [(92, 2), 87, 93]-NRT-code) | [i] | ||
| 14 | No linear OOA(1698, 92, F16, 2, 93) (dual of [(92, 2), 86, 94]-NRT-code) | [i] | ||
| 15 | No linear OOA(1699, 92, F16, 2, 94) (dual of [(92, 2), 85, 95]-NRT-code) | [i] | ||
| 16 | No linear OOA(16100, 92, F16, 2, 95) (dual of [(92, 2), 84, 96]-NRT-code) | [i] | ||
| 17 | No linear OOA(16101, 92, F16, 2, 96) (dual of [(92, 2), 83, 97]-NRT-code) | [i] | ||
| 18 | No linear OOA(16102, 92, F16, 2, 97) (dual of [(92, 2), 82, 98]-NRT-code) | [i] | ||
| 19 | No linear OOA(16103, 92, F16, 2, 98) (dual of [(92, 2), 81, 99]-NRT-code) | [i] | ||
| 20 | No linear OOA(16104, 92, F16, 2, 99) (dual of [(92, 2), 80, 100]-NRT-code) | [i] | ||
| 21 | No linear OOA(16105, 92, F16, 2, 100) (dual of [(92, 2), 79, 101]-NRT-code) | [i] | ||
| 22 | No linear OOA(16106, 92, F16, 2, 101) (dual of [(92, 2), 78, 102]-NRT-code) | [i] | ||
| 23 | No linear OOA(16107, 92, F16, 2, 102) (dual of [(92, 2), 77, 103]-NRT-code) | [i] | ||
| 24 | No linear OOA(16108, 92, F16, 2, 103) (dual of [(92, 2), 76, 104]-NRT-code) | [i] | ||
| 25 | No linear OOA(16109, 92, F16, 2, 104) (dual of [(92, 2), 75, 105]-NRT-code) | [i] | ||
| 26 | No linear OOA(16110, 92, F16, 2, 105) (dual of [(92, 2), 74, 106]-NRT-code) | [i] | ||
| 27 | No linear OOA(16111, 92, F16, 2, 106) (dual of [(92, 2), 73, 107]-NRT-code) | [i] | ||
| 28 | No linear OOA(16112, 92, F16, 2, 107) (dual of [(92, 2), 72, 108]-NRT-code) | [i] | ||
| 29 | No linear OOA(16113, 92, F16, 2, 108) (dual of [(92, 2), 71, 109]-NRT-code) | [i] | ||
| 30 | No linear OOA(16114, 92, F16, 2, 109) (dual of [(92, 2), 70, 110]-NRT-code) | [i] | ||
| 31 | No linear OOA(16115, 92, F16, 2, 110) (dual of [(92, 2), 69, 111]-NRT-code) | [i] | ||
| 32 | No linear OOA(16116, 92, F16, 2, 111) (dual of [(92, 2), 68, 112]-NRT-code) | [i] | ||
| 33 | No linear OOA(16117, 92, F16, 2, 112) (dual of [(92, 2), 67, 113]-NRT-code) | [i] | ||
| 34 | No linear OOA(16118, 92, F16, 2, 113) (dual of [(92, 2), 66, 114]-NRT-code) | [i] | ||
| 35 | No linear OOA(16119, 92, F16, 2, 114) (dual of [(92, 2), 65, 115]-NRT-code) | [i] | ||
| 36 | No linear OOA(16120, 92, F16, 2, 115) (dual of [(92, 2), 64, 116]-NRT-code) | [i] | ||
| 37 | No linear OOA(16121, 92, F16, 2, 116) (dual of [(92, 2), 63, 117]-NRT-code) | [i] | ||
| 38 | No linear OOA(16122, 92, F16, 2, 117) (dual of [(92, 2), 62, 118]-NRT-code) | [i] | ||
| 39 | No linear OOA(16123, 92, F16, 2, 118) (dual of [(92, 2), 61, 119]-NRT-code) | [i] | ||
| 40 | No linear OOA(16124, 92, F16, 2, 119) (dual of [(92, 2), 60, 120]-NRT-code) | [i] | ||
| 41 | No linear OOA(16125, 92, F16, 2, 120) (dual of [(92, 2), 59, 121]-NRT-code) | [i] | ||
| 42 | No linear OOA(16126, 92, F16, 2, 121) (dual of [(92, 2), 58, 122]-NRT-code) | [i] | ||
| 43 | No linear OOA(16127, 92, F16, 2, 122) (dual of [(92, 2), 57, 123]-NRT-code) | [i] | ||
| 44 | No linear OOA(16128, 92, F16, 2, 123) (dual of [(92, 2), 56, 124]-NRT-code) | [i] | ||
| 45 | No linear OOA(16129, 92, F16, 2, 124) (dual of [(92, 2), 55, 125]-NRT-code) | [i] | ||
| 46 | No linear OOA(16130, 92, F16, 2, 125) (dual of [(92, 2), 54, 126]-NRT-code) | [i] | ||
| 47 | No linear OOA(1685, 92, F16, 2, 80) (dual of [(92, 2), 99, 81]-NRT-code) | [i] | Depth Reduction | |
| 48 | No digital (5, 85, 92)-net over F16 | [i] | Extracting Embedded Orthogonal Array | |
| 49 | No linear OA(1686, 175, F16, 80) (dual of [175, 89, 81]-code) | [i] | Construction Y1 (Bound) | |