Information on Result #1183090
Digital (78, 87, 1195750)-net over F3, using net defined by OOA based on linear OOA(387, 1195750, F3, 9, 9) (dual of [(1195750, 9), 10761663, 10]-NRT-code), using
- OOA 4-folding and stacking with additional row [i] based on linear OA(387, 4783001, F3, 9) (dual of [4783001, 4782914, 10]-code), using
- 1 times code embedding in larger space [i] based on linear OA(386, 4783000, F3, 9) (dual of [4783000, 4782914, 10]-code), using
- construction X4 applied to C([0,4]) ⊂ C([0,3]) [i] based on
- linear OA(385, 4782970, F3, 9) (dual of [4782970, 4782885, 10]-code), using the expurgated narrow-sense BCH-code C(I) with length 4782970 | 328−1, defining interval I = [0,4], and minimum distance d ≥ |{−4,−3,…,4}|+1 = 10 (BCH-bound) [i]
- linear OA(357, 4782970, F3, 7) (dual of [4782970, 4782913, 8]-code), using the expurgated narrow-sense BCH-code C(I) with length 4782970 | 328−1, defining interval I = [0,3], and minimum distance d ≥ |{−3,−2,…,3}|+1 = 8 (BCH-bound) [i]
- linear OA(329, 30, F3, 29) (dual of [30, 1, 30]-code or 30-arc in PG(28,3)), using
- dual of repetition code with length 30 [i]
- linear OA(31, 30, F3, 1) (dual of [30, 29, 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([0,4]) ⊂ C([0,3]) [i] based on
- 1 times code embedding in larger space [i] based on linear OA(386, 4783000, F3, 9) (dual of [4783000, 4782914, 10]-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 (79, 88, 1195750)-net over F3 | [i] | Net Duplication | |
| 2 | Digital (80, 89, 1195750)-net over F3 | [i] | ||
| 3 | Digital (105, 114, 2391500)-net over F3 | [i] | (u, u+v)-Construction for Nets | |