Information on Result #1843341
(82, 97, 1897424)-net in base 32, using (u, u+v)-construction based on
- (21, 28, 699053)-net in base 32, using
- base change [i] based on digital (13, 20, 699053)-net over F128, using
- net defined by OOA [i] based on linear OOA(12820, 699053, F128, 7, 7) (dual of [(699053, 7), 4893351, 8]-NRT-code), using
- OOA 3-folding and stacking with additional row [i] based on linear OA(12820, 2097160, F128, 7) (dual of [2097160, 2097140, 8]-code), using
- construction X applied to C([0,3]) ⊂ C([0,2]) [i] based on
- linear OA(12819, 2097153, F128, 7) (dual of [2097153, 2097134, 8]-code), using the expurgated narrow-sense BCH-code C(I) with length 2097153 | 1286−1, defining interval I = [0,3], and minimum distance d ≥ |{−3,−2,…,3}|+1 = 8 (BCH-bound) [i]
- linear OA(12813, 2097153, F128, 5) (dual of [2097153, 2097140, 6]-code), using the expurgated narrow-sense BCH-code C(I) with length 2097153 | 1286−1, defining interval I = [0,2], and minimum distance d ≥ |{−2,−1,0,1,2}|+1 = 6 (BCH-bound) [i]
- linear OA(1281, 7, F128, 1) (dual of [7, 6, 2]-code), using
- discarding factors / shortening the dual code based on linear OA(1281, s, F128, 1) (dual of [s, s−1, 2]-code) for arbitrarily large s, using
- construction X applied to C([0,3]) ⊂ C([0,2]) [i] based on
- OOA 3-folding and stacking with additional row [i] based on linear OA(12820, 2097160, F128, 7) (dual of [2097160, 2097140, 8]-code), using
- net defined by OOA [i] based on linear OOA(12820, 699053, F128, 7, 7) (dual of [(699053, 7), 4893351, 8]-NRT-code), using
- base change [i] based on digital (13, 20, 699053)-net over F128, using
- (54, 69, 1198371)-net in base 32, using
- net defined by OOA [i] based on OOA(3269, 1198371, S32, 15, 15), using
- OOA 7-folding and stacking with additional row [i] based on OA(3269, 8388598, S32, 15), using
- discarding factors based on OA(3269, large, S32, 15), using
- discarding parts of the base [i] based on linear OA(6457, large, F64, 15) (dual of [large, large−57, 16]-code), using
- the expurgated narrow-sense BCH-code C(I) with length 16777217 | 648−1, defining interval I = [0,7], and minimum distance d ≥ |{−7,−6,…,7}|+1 = 16 (BCH-bound) [i]
- discarding parts of the base [i] based on linear OA(6457, large, F64, 15) (dual of [large, large−57, 16]-code), using
- discarding factors based on OA(3269, large, S32, 15), using
- OOA 7-folding and stacking with additional row [i] based on OA(3269, 8388598, S32, 15), using
- net defined by OOA [i] based on OOA(3269, 1198371, S32, 15, 15), using
Mode: Constructive.
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 | (83, 98, 1897424)-net in base 32 | [i] | Net Duplication | |