Information on Result #1186812
Digital (81, 100, 1822)-net over F4, using net defined by OOA based on linear OOA(4100, 1822, F4, 19, 19) (dual of [(1822, 19), 34518, 20]-NRT-code), using
- OOA 9-folding and stacking with additional row [i] based on linear OA(4100, 16399, F4, 19) (dual of [16399, 16299, 20]-code), using
- discarding factors / shortening the dual code based on linear OA(4100, 16400, F4, 19) (dual of [16400, 16300, 20]-code), using
- construction X applied to C([0,9]) ⊂ C([0,8]) [i] based on
- linear OA(499, 16385, F4, 19) (dual of [16385, 16286, 20]-code), using the expurgated narrow-sense BCH-code C(I) with length 16385 | 414−1, defining interval I = [0,9], and minimum distance d ≥ |{−9,−8,…,9}|+1 = 20 (BCH-bound) [i]
- linear OA(485, 16385, F4, 17) (dual of [16385, 16300, 18]-code), using the expurgated narrow-sense BCH-code C(I) with length 16385 | 414−1, defining interval I = [0,8], and minimum distance d ≥ |{−8,−7,…,8}|+1 = 18 (BCH-bound) [i]
- linear OA(41, 15, F4, 1) (dual of [15, 14, 2]-code), using
- discarding factors / shortening the dual code based on linear OA(41, s, F4, 1) (dual of [s, s−1, 2]-code) for arbitrarily large s, using
- construction X applied to C([0,9]) ⊂ C([0,8]) [i] based on
- discarding factors / shortening the dual code based on linear OA(4100, 16400, F4, 19) (dual of [16400, 16300, 20]-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 (82, 101, 1822)-net over F4 | [i] | Net Duplication | |
| 2 | Digital (83, 102, 1822)-net over F4 | [i] | ||
| 3 | Digital (84, 103, 1822)-net over F4 | [i] | ||