Information on Result #548036
There is no linear OA(1668, 77, F16, 64) (dual of [77, 9, 65]-code), because construction Y1 would yield
- OA(1667, 69, S16, 64), but
- the (dual) Plotkin bound shows that M ≥ 7588 550360 256754 183279 148073 529370 729071 901715 047420 004889 892225 542594 864082 845696 / 13 > 1667 [i]
- OA(169, 77, S16, 8), but
- the Rao or (dual) Hamming bound shows that M ≥ 68757 087631 > 169 [i]
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(1669, 78, F16, 65) (dual of [78, 9, 66]-code) | [i] | Truncation | |
| 2 | No linear OOA(1669, 77, F16, 2, 65) (dual of [(77, 2), 85, 66]-NRT-code) | [i] | m-Reduction for OOAs | |
| 3 | No linear OOA(1671, 77, F16, 2, 67) (dual of [(77, 2), 83, 68]-NRT-code) | [i] | ||
| 4 | No linear OOA(1672, 77, F16, 2, 68) (dual of [(77, 2), 82, 69]-NRT-code) | [i] | ||
| 5 | No linear OOA(1673, 77, F16, 2, 69) (dual of [(77, 2), 81, 70]-NRT-code) | [i] | ||
| 6 | No linear OOA(1674, 77, F16, 2, 70) (dual of [(77, 2), 80, 71]-NRT-code) | [i] | ||
| 7 | No linear OOA(1675, 77, F16, 2, 71) (dual of [(77, 2), 79, 72]-NRT-code) | [i] | ||
| 8 | No linear OOA(1676, 77, F16, 2, 72) (dual of [(77, 2), 78, 73]-NRT-code) | [i] | ||
| 9 | No linear OOA(1677, 77, F16, 2, 73) (dual of [(77, 2), 77, 74]-NRT-code) | [i] | ||
| 10 | No linear OOA(1678, 77, F16, 2, 74) (dual of [(77, 2), 76, 75]-NRT-code) | [i] | ||
| 11 | No linear OOA(1679, 77, F16, 2, 75) (dual of [(77, 2), 75, 76]-NRT-code) | [i] | ||
| 12 | No linear OOA(1680, 77, F16, 2, 76) (dual of [(77, 2), 74, 77]-NRT-code) | [i] | ||
| 13 | No linear OOA(1681, 77, F16, 2, 77) (dual of [(77, 2), 73, 78]-NRT-code) | [i] | ||
| 14 | No linear OOA(1682, 77, F16, 2, 78) (dual of [(77, 2), 72, 79]-NRT-code) | [i] | ||
| 15 | No linear OOA(1683, 77, F16, 2, 79) (dual of [(77, 2), 71, 80]-NRT-code) | [i] | ||
| 16 | No linear OOA(1684, 77, F16, 2, 80) (dual of [(77, 2), 70, 81]-NRT-code) | [i] | ||
| 17 | No linear OOA(1685, 77, F16, 2, 81) (dual of [(77, 2), 69, 82]-NRT-code) | [i] | ||
| 18 | No linear OOA(1686, 77, F16, 2, 82) (dual of [(77, 2), 68, 83]-NRT-code) | [i] | ||
| 19 | No linear OOA(1687, 77, F16, 2, 83) (dual of [(77, 2), 67, 84]-NRT-code) | [i] | ||
| 20 | No linear OOA(1688, 77, F16, 2, 84) (dual of [(77, 2), 66, 85]-NRT-code) | [i] | ||
| 21 | No linear OOA(1689, 77, F16, 2, 85) (dual of [(77, 2), 65, 86]-NRT-code) | [i] | ||
| 22 | No linear OOA(1690, 77, F16, 2, 86) (dual of [(77, 2), 64, 87]-NRT-code) | [i] | ||
| 23 | No linear OOA(1691, 77, F16, 2, 87) (dual of [(77, 2), 63, 88]-NRT-code) | [i] | ||
| 24 | No linear OOA(1692, 77, F16, 2, 88) (dual of [(77, 2), 62, 89]-NRT-code) | [i] | ||
| 25 | No linear OOA(1693, 77, F16, 2, 89) (dual of [(77, 2), 61, 90]-NRT-code) | [i] | ||
| 26 | No linear OOA(1694, 77, F16, 2, 90) (dual of [(77, 2), 60, 91]-NRT-code) | [i] | ||
| 27 | No linear OOA(1695, 77, F16, 2, 91) (dual of [(77, 2), 59, 92]-NRT-code) | [i] | ||
| 28 | No linear OOA(1696, 77, F16, 2, 92) (dual of [(77, 2), 58, 93]-NRT-code) | [i] | ||
| 29 | No linear OOA(1697, 77, F16, 2, 93) (dual of [(77, 2), 57, 94]-NRT-code) | [i] | ||
| 30 | No linear OOA(1698, 77, F16, 2, 94) (dual of [(77, 2), 56, 95]-NRT-code) | [i] | ||
| 31 | No linear OOA(1699, 77, F16, 2, 95) (dual of [(77, 2), 55, 96]-NRT-code) | [i] | ||
| 32 | No linear OOA(16100, 77, F16, 2, 96) (dual of [(77, 2), 54, 97]-NRT-code) | [i] | ||
| 33 | No linear OOA(16101, 77, F16, 2, 97) (dual of [(77, 2), 53, 98]-NRT-code) | [i] | ||
| 34 | No linear OOA(16102, 77, F16, 2, 98) (dual of [(77, 2), 52, 99]-NRT-code) | [i] | ||
| 35 | No linear OOA(16103, 77, F16, 2, 99) (dual of [(77, 2), 51, 100]-NRT-code) | [i] | ||
| 36 | No linear OOA(16104, 77, F16, 2, 100) (dual of [(77, 2), 50, 101]-NRT-code) | [i] | ||
| 37 | No linear OOA(16105, 77, F16, 2, 101) (dual of [(77, 2), 49, 102]-NRT-code) | [i] | ||
| 38 | No linear OOA(16106, 77, F16, 2, 102) (dual of [(77, 2), 48, 103]-NRT-code) | [i] | ||
| 39 | No linear OOA(16107, 77, F16, 2, 103) (dual of [(77, 2), 47, 104]-NRT-code) | [i] | ||
| 40 | No linear OOA(16108, 77, F16, 2, 104) (dual of [(77, 2), 46, 105]-NRT-code) | [i] | ||
| 41 | No linear OOA(16109, 77, F16, 2, 105) (dual of [(77, 2), 45, 106]-NRT-code) | [i] | ||
| 42 | No linear OOA(16110, 77, F16, 2, 106) (dual of [(77, 2), 44, 107]-NRT-code) | [i] | ||
| 43 | No linear OOA(16111, 77, F16, 2, 107) (dual of [(77, 2), 43, 108]-NRT-code) | [i] | ||
| 44 | No linear OOA(16112, 77, F16, 2, 108) (dual of [(77, 2), 42, 109]-NRT-code) | [i] | ||
| 45 | No linear OOA(16113, 77, F16, 2, 109) (dual of [(77, 2), 41, 110]-NRT-code) | [i] | ||
| 46 | No linear OOA(16114, 77, F16, 2, 110) (dual of [(77, 2), 40, 111]-NRT-code) | [i] | ||
| 47 | No linear OOA(16115, 77, F16, 2, 111) (dual of [(77, 2), 39, 112]-NRT-code) | [i] | ||
| 48 | No linear OOA(16116, 77, F16, 2, 112) (dual of [(77, 2), 38, 113]-NRT-code) | [i] | ||
| 49 | No linear OOA(16117, 77, F16, 2, 113) (dual of [(77, 2), 37, 114]-NRT-code) | [i] | ||
| 50 | No linear OOA(16118, 77, F16, 2, 114) (dual of [(77, 2), 36, 115]-NRT-code) | [i] | ||
| 51 | No linear OOA(16119, 77, F16, 2, 115) (dual of [(77, 2), 35, 116]-NRT-code) | [i] | ||
| 52 | No linear OOA(16120, 77, F16, 2, 116) (dual of [(77, 2), 34, 117]-NRT-code) | [i] | ||
| 53 | No linear OOA(16121, 77, F16, 2, 117) (dual of [(77, 2), 33, 118]-NRT-code) | [i] | ||
| 54 | No linear OOA(16122, 77, F16, 2, 118) (dual of [(77, 2), 32, 119]-NRT-code) | [i] | ||
| 55 | No linear OOA(16123, 77, F16, 2, 119) (dual of [(77, 2), 31, 120]-NRT-code) | [i] | ||
| 56 | No linear OOA(16124, 77, F16, 2, 120) (dual of [(77, 2), 30, 121]-NRT-code) | [i] | ||
| 57 | No linear OOA(16125, 77, F16, 2, 121) (dual of [(77, 2), 29, 122]-NRT-code) | [i] | ||
| 58 | No linear OOA(16126, 77, F16, 2, 122) (dual of [(77, 2), 28, 123]-NRT-code) | [i] | ||
| 59 | No linear OOA(16127, 77, F16, 2, 123) (dual of [(77, 2), 27, 124]-NRT-code) | [i] | ||
| 60 | No linear OOA(16128, 77, F16, 2, 124) (dual of [(77, 2), 26, 125]-NRT-code) | [i] | ||
| 61 | No linear OOA(16129, 77, F16, 2, 125) (dual of [(77, 2), 25, 126]-NRT-code) | [i] | ||
| 62 | No linear OOA(16130, 77, F16, 2, 126) (dual of [(77, 2), 24, 127]-NRT-code) | [i] | ||
| 63 | No linear OOA(1668, 77, F16, 2, 64) (dual of [(77, 2), 86, 65]-NRT-code) | [i] | Depth Reduction | |
| 64 | No digital (4, 68, 77)-net over F16 | [i] | Extracting Embedded Orthogonal Array | |