Information on Result #548594
There is no linear OA(3108, 117, F3, 72) (dual of [117, 9, 73]-code), because construction Y1 would yield
- linear OA(3107, 113, F3, 72) (dual of [113, 6, 73]-code), but
- residual code [i] would yield linear OA(335, 40, F3, 24) (dual of [40, 5, 25]-code), but
- “vE1†bound on codes from Brouwer’s database [i]
- residual code [i] would yield linear OA(335, 40, F3, 24) (dual of [40, 5, 25]-code), but
- OA(39, 117, S3, 4), but
- discarding factors would yield OA(39, 100, S3, 4), but
- the Rao or (dual) Hamming bound shows that M ≥ 20001 > 39 [i]
- discarding factors would yield OA(39, 100, S3, 4), 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(3109, 117, F3, 2, 73) (dual of [(117, 2), 125, 74]-NRT-code) | [i] | m-Reduction for OOAs | |
| 2 | No linear OOA(3110, 117, F3, 2, 74) (dual of [(117, 2), 124, 75]-NRT-code) | [i] | ||
| 3 | No linear OOA(3112, 117, F3, 2, 76) (dual of [(117, 2), 122, 77]-NRT-code) | [i] | ||
| 4 | No linear OOA(3113, 117, F3, 2, 77) (dual of [(117, 2), 121, 78]-NRT-code) | [i] | ||
| 5 | No linear OOA(3114, 117, F3, 2, 78) (dual of [(117, 2), 120, 79]-NRT-code) | [i] | ||
| 6 | No linear OOA(3115, 117, F3, 2, 79) (dual of [(117, 2), 119, 80]-NRT-code) | [i] | ||
| 7 | No linear OOA(3116, 117, F3, 2, 80) (dual of [(117, 2), 118, 81]-NRT-code) | [i] | ||
| 8 | No linear OOA(3117, 117, F3, 2, 81) (dual of [(117, 2), 117, 82]-NRT-code) | [i] | ||
| 9 | No linear OOA(3118, 117, F3, 2, 82) (dual of [(117, 2), 116, 83]-NRT-code) | [i] | ||
| 10 | No linear OOA(3119, 117, F3, 2, 83) (dual of [(117, 2), 115, 84]-NRT-code) | [i] | ||
| 11 | No linear OOA(3120, 117, F3, 2, 84) (dual of [(117, 2), 114, 85]-NRT-code) | [i] | ||
| 12 | No linear OOA(3121, 117, F3, 2, 85) (dual of [(117, 2), 113, 86]-NRT-code) | [i] | ||
| 13 | No linear OOA(3122, 117, F3, 2, 86) (dual of [(117, 2), 112, 87]-NRT-code) | [i] | ||
| 14 | No linear OOA(3123, 117, F3, 2, 87) (dual of [(117, 2), 111, 88]-NRT-code) | [i] | ||
| 15 | No linear OOA(3124, 117, F3, 2, 88) (dual of [(117, 2), 110, 89]-NRT-code) | [i] | ||
| 16 | No linear OOA(3125, 117, F3, 2, 89) (dual of [(117, 2), 109, 90]-NRT-code) | [i] | ||
| 17 | No linear OOA(3126, 117, F3, 2, 90) (dual of [(117, 2), 108, 91]-NRT-code) | [i] | ||
| 18 | No linear OOA(3127, 117, F3, 2, 91) (dual of [(117, 2), 107, 92]-NRT-code) | [i] | ||
| 19 | No linear OOA(3128, 117, F3, 2, 92) (dual of [(117, 2), 106, 93]-NRT-code) | [i] | ||
| 20 | No linear OOA(3129, 117, F3, 2, 93) (dual of [(117, 2), 105, 94]-NRT-code) | [i] | ||
| 21 | No linear OOA(3130, 117, F3, 2, 94) (dual of [(117, 2), 104, 95]-NRT-code) | [i] | ||
| 22 | No linear OOA(3131, 117, F3, 2, 95) (dual of [(117, 2), 103, 96]-NRT-code) | [i] | ||
| 23 | No linear OOA(3132, 117, F3, 2, 96) (dual of [(117, 2), 102, 97]-NRT-code) | [i] | ||
| 24 | No linear OOA(3133, 117, F3, 2, 97) (dual of [(117, 2), 101, 98]-NRT-code) | [i] | ||
| 25 | No linear OOA(3134, 117, F3, 2, 98) (dual of [(117, 2), 100, 99]-NRT-code) | [i] | ||
| 26 | No linear OOA(3135, 117, F3, 2, 99) (dual of [(117, 2), 99, 100]-NRT-code) | [i] | ||
| 27 | No linear OOA(3136, 117, F3, 2, 100) (dual of [(117, 2), 98, 101]-NRT-code) | [i] | ||
| 28 | No linear OOA(3137, 117, F3, 2, 101) (dual of [(117, 2), 97, 102]-NRT-code) | [i] | ||
| 29 | No linear OOA(3138, 117, F3, 2, 102) (dual of [(117, 2), 96, 103]-NRT-code) | [i] | ||
| 30 | No linear OOA(3139, 117, F3, 2, 103) (dual of [(117, 2), 95, 104]-NRT-code) | [i] | ||
| 31 | No linear OOA(3140, 117, F3, 2, 104) (dual of [(117, 2), 94, 105]-NRT-code) | [i] | ||
| 32 | No linear OOA(3141, 117, F3, 2, 105) (dual of [(117, 2), 93, 106]-NRT-code) | [i] | ||
| 33 | No linear OOA(3142, 117, F3, 2, 106) (dual of [(117, 2), 92, 107]-NRT-code) | [i] | ||
| 34 | No linear OOA(3143, 117, F3, 2, 107) (dual of [(117, 2), 91, 108]-NRT-code) | [i] | ||
| 35 | No linear OOA(3144, 117, F3, 2, 108) (dual of [(117, 2), 90, 109]-NRT-code) | [i] | ||
| 36 | No linear OOA(3145, 117, F3, 2, 109) (dual of [(117, 2), 89, 110]-NRT-code) | [i] | ||
| 37 | No linear OOA(3146, 117, F3, 2, 110) (dual of [(117, 2), 88, 111]-NRT-code) | [i] | ||
| 38 | No linear OOA(3147, 117, F3, 2, 111) (dual of [(117, 2), 87, 112]-NRT-code) | [i] | ||
| 39 | No linear OOA(3148, 117, F3, 2, 112) (dual of [(117, 2), 86, 113]-NRT-code) | [i] | ||
| 40 | No linear OOA(3149, 117, F3, 2, 113) (dual of [(117, 2), 85, 114]-NRT-code) | [i] | ||
| 41 | No linear OOA(3150, 117, F3, 2, 114) (dual of [(117, 2), 84, 115]-NRT-code) | [i] | ||
| 42 | No linear OOA(3151, 117, F3, 2, 115) (dual of [(117, 2), 83, 116]-NRT-code) | [i] | ||
| 43 | No linear OOA(3152, 117, F3, 2, 116) (dual of [(117, 2), 82, 117]-NRT-code) | [i] | ||
| 44 | No linear OOA(3153, 117, F3, 2, 117) (dual of [(117, 2), 81, 118]-NRT-code) | [i] | ||
| 45 | No linear OOA(3154, 117, F3, 2, 118) (dual of [(117, 2), 80, 119]-NRT-code) | [i] | ||
| 46 | No linear OOA(3155, 117, F3, 2, 119) (dual of [(117, 2), 79, 120]-NRT-code) | [i] | ||
| 47 | No linear OOA(3156, 117, F3, 2, 120) (dual of [(117, 2), 78, 121]-NRT-code) | [i] | ||
| 48 | No linear OOA(3157, 117, F3, 2, 121) (dual of [(117, 2), 77, 122]-NRT-code) | [i] | ||
| 49 | No linear OOA(3158, 117, F3, 2, 122) (dual of [(117, 2), 76, 123]-NRT-code) | [i] | ||
| 50 | No linear OOA(3159, 117, F3, 2, 123) (dual of [(117, 2), 75, 124]-NRT-code) | [i] | ||
| 51 | No linear OOA(3160, 117, F3, 2, 124) (dual of [(117, 2), 74, 125]-NRT-code) | [i] | ||
| 52 | No linear OOA(3161, 117, F3, 2, 125) (dual of [(117, 2), 73, 126]-NRT-code) | [i] | ||
| 53 | No linear OOA(3162, 117, F3, 2, 126) (dual of [(117, 2), 72, 127]-NRT-code) | [i] | ||
| 54 | No linear OOA(3163, 117, F3, 2, 127) (dual of [(117, 2), 71, 128]-NRT-code) | [i] | ||
| 55 | No linear OOA(3164, 117, F3, 2, 128) (dual of [(117, 2), 70, 129]-NRT-code) | [i] | ||
| 56 | No linear OOA(3165, 117, F3, 2, 129) (dual of [(117, 2), 69, 130]-NRT-code) | [i] | ||
| 57 | No linear OOA(3166, 117, F3, 2, 130) (dual of [(117, 2), 68, 131]-NRT-code) | [i] | ||
| 58 | No linear OOA(3167, 117, F3, 2, 131) (dual of [(117, 2), 67, 132]-NRT-code) | [i] | ||
| 59 | No linear OOA(3168, 117, F3, 2, 132) (dual of [(117, 2), 66, 133]-NRT-code) | [i] | ||
| 60 | No linear OOA(3169, 117, F3, 2, 133) (dual of [(117, 2), 65, 134]-NRT-code) | [i] | ||
| 61 | No linear OOA(3170, 117, F3, 2, 134) (dual of [(117, 2), 64, 135]-NRT-code) | [i] | ||
| 62 | No linear OOA(3171, 117, F3, 2, 135) (dual of [(117, 2), 63, 136]-NRT-code) | [i] | ||
| 63 | No linear OOA(3172, 117, F3, 2, 136) (dual of [(117, 2), 62, 137]-NRT-code) | [i] | ||
| 64 | No linear OOA(3173, 117, F3, 2, 137) (dual of [(117, 2), 61, 138]-NRT-code) | [i] | ||
| 65 | No linear OOA(3174, 117, F3, 2, 138) (dual of [(117, 2), 60, 139]-NRT-code) | [i] | ||
| 66 | No linear OOA(3175, 117, F3, 2, 139) (dual of [(117, 2), 59, 140]-NRT-code) | [i] | ||
| 67 | No linear OOA(3176, 117, F3, 2, 140) (dual of [(117, 2), 58, 141]-NRT-code) | [i] | ||
| 68 | No linear OOA(3177, 117, F3, 2, 141) (dual of [(117, 2), 57, 142]-NRT-code) | [i] | ||
| 69 | No linear OOA(3108, 117, F3, 2, 72) (dual of [(117, 2), 126, 73]-NRT-code) | [i] | Depth Reduction | |
| 70 | No linear OOA(3108, 117, F3, 3, 72) (dual of [(117, 3), 243, 73]-NRT-code) | [i] | ||
| 71 | No linear OOA(3108, 117, F3, 4, 72) (dual of [(117, 4), 360, 73]-NRT-code) | [i] | ||
| 72 | No linear OOA(3108, 117, F3, 5, 72) (dual of [(117, 5), 477, 73]-NRT-code) | [i] | ||
| 73 | No digital (36, 108, 117)-net over F3 | [i] | Extracting Embedded Orthogonal Array | |