Information on Result #1184106
Digital (127, 142, 683285)-net over F3, using net defined by OOA based on linear OOA(3142, 683285, F3, 15, 15) (dual of [(683285, 15), 10249133, 16]-NRT-code), using
- OOA 7-folding and stacking with additional row [i] based on linear OA(3142, 4782996, F3, 15) (dual of [4782996, 4782854, 16]-code), using
- discarding factors / shortening the dual code based on linear OA(3142, 4782999, F3, 15) (dual of [4782999, 4782857, 16]-code), using
- construction X applied to C([0,7]) ⊂ C([0,6]) [i] based on
- linear OA(3141, 4782970, F3, 15) (dual of [4782970, 4782829, 16]-code), using the expurgated narrow-sense BCH-code C(I) with length 4782970 | 328−1, defining interval I = [0,7], and minimum distance d ≥ |{−7,−6,…,7}|+1 = 16 (BCH-bound) [i]
- linear OA(3113, 4782970, F3, 13) (dual of [4782970, 4782857, 14]-code), using the expurgated narrow-sense BCH-code C(I) with length 4782970 | 328−1, defining interval I = [0,6], and minimum distance d ≥ |{−6,−5,…,6}|+1 = 14 (BCH-bound) [i]
- linear OA(31, 29, F3, 1) (dual of [29, 28, 2]-code), using
- discarding factors / shortening the dual code based on linear OA(31, s, F3, 1) (dual of [s, s−1, 2]-code) for arbitrarily large s, using
- construction X applied to C([0,7]) ⊂ C([0,6]) [i] based on
- discarding factors / shortening the dual code based on linear OA(3142, 4782999, F3, 15) (dual of [4782999, 4782857, 16]-code), using
Mode: Constructive and linear.
Optimality
Show details for fixed k and m, k and s, k and t, m and s, m and t, t and s.
Other Results with Identical Parameters
None.
Depending Results
The following results depend on this result:
| Result | This result only | Method | ||
|---|---|---|---|---|
| 1 | Digital (128, 143, 683285)-net over F3 | [i] | Net Duplication | |
| 2 | Digital (129, 144, 683285)-net over F3 | [i] | ||