Information on Result #1190666
Digital (41, 58, 301)-net over F7, using net defined by OOA based on linear OOA(758, 301, F7, 17, 17) (dual of [(301, 17), 5059, 18]-NRT-code), using
- OOA 8-folding and stacking with additional row [i] based on linear OA(758, 2409, F7, 17) (dual of [2409, 2351, 18]-code), using
- discarding factors / shortening the dual code based on linear OA(758, 2411, F7, 17) (dual of [2411, 2353, 18]-code), using
- construction X applied to C([0,8]) ⊂ C([0,7]) [i] based on
- linear OA(757, 2402, F7, 17) (dual of [2402, 2345, 18]-code), using the expurgated narrow-sense BCH-code C(I) with length 2402 | 78−1, defining interval I = [0,8], and minimum distance d ≥ |{−8,−7,…,8}|+1 = 18 (BCH-bound) [i]
- linear OA(749, 2402, F7, 15) (dual of [2402, 2353, 16]-code), using the expurgated narrow-sense BCH-code C(I) with length 2402 | 78−1, defining interval I = [0,7], and minimum distance d ≥ |{−7,−6,…,7}|+1 = 16 (BCH-bound) [i]
- linear OA(71, 9, F7, 1) (dual of [9, 8, 2]-code), using
- discarding factors / shortening the dual code based on linear OA(71, s, F7, 1) (dual of [s, s−1, 2]-code) for arbitrarily large s, using
- construction X applied to C([0,8]) ⊂ C([0,7]) [i] based on
- discarding factors / shortening the dual code based on linear OA(758, 2411, F7, 17) (dual of [2411, 2353, 18]-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 (42, 59, 301)-net over F7 | [i] | Net Duplication | |
| 2 | Digital (43, 60, 301)-net over F7 | [i] | ||