Information on Result #1184054
Digital (79, 94, 2815)-net over F3, using net defined by OOA based on linear OOA(394, 2815, F3, 15, 15) (dual of [(2815, 15), 42131, 16]-NRT-code), using
- OOA 7-folding and stacking with additional row [i] based on linear OA(394, 19706, F3, 15) (dual of [19706, 19612, 16]-code), using
- 2 times code embedding in larger space [i] based on linear OA(392, 19704, F3, 15) (dual of [19704, 19612, 16]-code), using
- construction X4 applied to C([0,7]) ⊂ C([0,6]) [i] based on
- linear OA(391, 19684, F3, 15) (dual of [19684, 19593, 16]-code), using the expurgated narrow-sense BCH-code C(I) with length 19684 | 318−1, defining interval I = [0,7], and minimum distance d ≥ |{−7,−6,…,7}|+1 = 16 (BCH-bound) [i]
- linear OA(373, 19684, F3, 13) (dual of [19684, 19611, 14]-code), using the expurgated narrow-sense BCH-code C(I) with length 19684 | 318−1, defining interval I = [0,6], and minimum distance d ≥ |{−6,−5,…,6}|+1 = 14 (BCH-bound) [i]
- linear OA(319, 20, F3, 19) (dual of [20, 1, 20]-code or 20-arc in PG(18,3)), using
- dual of repetition code with length 20 [i]
- linear OA(31, 20, F3, 1) (dual of [20, 19, 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 X4 applied to C([0,7]) ⊂ C([0,6]) [i] based on
- 2 times code embedding in larger space [i] based on linear OA(392, 19704, F3, 15) (dual of [19704, 19612, 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 (80, 95, 2815)-net over F3 | [i] | Net Duplication | |
| 2 | Digital (81, 96, 2815)-net over F3 | [i] | ||