Information on Result #1234931
Linear OOA(396, large, F3, 4, 7), using extracting embedded OOA based on digital (89, 96, large)-net over F3, using
- (u, u+v)-construction [i] based on
- digital (0, 3, 4)-net over F3, using
- net from sequence [i] based on digital (0, 3)-sequence over F3, using
- Faure sequence [i]
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F3 with g(F) = 0 and N(F) ≥ 4, using
- the rational function field F3(x) [i]
- Niederreiter sequence [i]
- net from sequence [i] based on digital (0, 3)-sequence over F3, using
- digital (86, 93, 8388600)-net over F3, using
- trace code for nets [i] based on digital (24, 31, 2796200)-net over F27, using
- net defined by OOA [i] based on linear OOA(2731, 2796200, F27, 7, 7) (dual of [(2796200, 7), 19573369, 8]-NRT-code), using
- OOA 3-folding and stacking with additional row [i] based on linear OA(2731, 8388601, F27, 7) (dual of [8388601, 8388570, 8]-code), using
- discarding factors / shortening the dual code based on linear OA(2731, large, F27, 7) (dual of [large, large−31, 8]-code), using
- the expurgated narrow-sense BCH-code C(I) with length 14348908 | 2710−1, defining interval I = [0,3], and minimum distance d ≥ |{−3,−2,…,3}|+1 = 8 (BCH-bound) [i]
- discarding factors / shortening the dual code based on linear OA(2731, large, F27, 7) (dual of [large, large−31, 8]-code), using
- OOA 3-folding and stacking with additional row [i] based on linear OA(2731, 8388601, F27, 7) (dual of [8388601, 8388570, 8]-code), using
- net defined by OOA [i] based on linear OOA(2731, 2796200, F27, 7, 7) (dual of [(2796200, 7), 19573369, 8]-NRT-code), using
- trace code for nets [i] based on digital (24, 31, 2796200)-net over F27, using
- digital (0, 3, 4)-net over F3, using
Mode: Constructive and linear.
Optimality
Show details for fixed k and m, k and t, m and t.
Other Results with Identical Parameters
None.
Depending Results
The following results depend on this result:
| Result | This result only | Method | ||
|---|---|---|---|---|
| 1 | Linear OOA(396, large, F3, 4, 6) | [i] | Strength Reduction for OOAs | |
| 2 | Linear OOA(396, large, F3, 4, 5) | [i] | ||
| 3 | Linear OOA(396, large, F3, 4, 4) | [i] | ||
| 4 | Linear OOA(396, large, F3, 4, 3) | [i] | ||
| 5 | Linear OOA(3100, large, F3, 4, 7) | [i] | NRT-Code Embedding in Larger Space | |
| 6 | Linear OOA(3104, large, F3, 4, 7) | [i] | ||
| 7 | Linear OOA(3108, large, F3, 4, 7) | [i] | ||
| 8 | Linear OOA(3112, large, F3, 4, 7) | [i] | ||
| 9 | Linear OOA(3116, large, F3, 4, 7) | [i] | ||
| 10 | Linear OOA(3128, large, F3, 4, 7) | [i] | ||
| 11 | Linear OOA(3132, large, F3, 4, 7) | [i] | ||
| 12 | Linear OOA(3144, large, F3, 4, 7) | [i] | ||
| 13 | Linear OOA(3148, large, F3, 4, 7) | [i] | ||
| 14 | Linear OOA(3152, large, F3, 4, 7) | [i] | ||
| 15 | Linear OOA(3160, large, F3, 4, 7) | [i] | ||
| 16 | Linear OOA(3164, large, F3, 4, 7) | [i] | ||
| 17 | Linear OOA(3168, large, F3, 4, 7) | [i] | ||
| 18 | Linear OOA(3176, large, F3, 4, 7) | [i] | ||
| 19 | Linear OOA(3180, large, F3, 4, 7) | [i] | ||
| 20 | Linear OOA(3184, large, F3, 4, 7) | [i] | ||
| 21 | Linear OOA(3192, large, F3, 4, 7) | [i] | ||
| 22 | Linear OOA(3196, large, F3, 4, 7) | [i] | ||
| 23 | Linear OOA(3200, large, F3, 4, 7) | [i] | ||
| 24 | Linear OOA(3208, large, F3, 4, 7) | [i] | ||
| 25 | Linear OOA(3212, large, F3, 4, 7) | [i] | ||
| 26 | Linear OOA(3216, large, F3, 4, 7) | [i] | ||
| 27 | Linear OOA(3224, large, F3, 4, 7) | [i] | ||
| 28 | Linear OOA(3228, large, F3, 4, 7) | [i] | ||
| 29 | Linear OOA(3232, large, F3, 4, 7) | [i] | ||
| 30 | Linear OOA(3240, large, F3, 4, 7) | [i] | ||
| 31 | Linear OOA(3244, large, F3, 4, 7) | [i] | ||
| 32 | Linear OOA(3248, large, F3, 4, 7) | [i] | ||
| 33 | Linear OOA(397, large, F3, 4, 7) | [i] | OOA Duplication | |
| 34 | Linear OOA(398, large, F3, 4, 7) | [i] | ||