Information on Result #3188653
Digital (201, 217, 1048653)-net over F2, using t-expansion based on digital (200, 217, 1048653)-net over F2, using
- (u, u+v)-construction [i] based on
- digital (24, 32, 78)-net over F2, using
- net defined by OOA [i] based on linear OOA(232, 78, F2, 8, 8) (dual of [(78, 8), 592, 9]-NRT-code), using
- appending kth column [i] based on linear OOA(232, 78, F2, 7, 8) (dual of [(78, 7), 514, 9]-NRT-code), using
- (u, u+v)-construction [i] based on
- linear OOA(211, 47, F2, 7, 4) (dual of [(47, 7), 318, 5]-NRT-code), using
- appending 3 arbitrary columns [i] based on linear OOA(211, 47, F2, 4, 4) (dual of [(47, 4), 177, 5]-NRT-code), using
- appending kth column [i] based on linear OOA(211, 47, F2, 3, 4) (dual of [(47, 3), 130, 5]-NRT-code), using
- extracting embedded OOA [i] based on digital (7, 11, 47)-net over F2, using
- appending kth column [i] based on linear OOA(211, 47, F2, 3, 4) (dual of [(47, 3), 130, 5]-NRT-code), using
- appending 3 arbitrary columns [i] based on linear OOA(211, 47, F2, 4, 4) (dual of [(47, 4), 177, 5]-NRT-code), using
- linear OOA(221, 39, F2, 7, 8) (dual of [(39, 7), 252, 9]-NRT-code), using
- extracting embedded OOA [i] based on digital (13, 21, 39)-net over F2, using
- linear OOA(211, 47, F2, 7, 4) (dual of [(47, 7), 318, 5]-NRT-code), using
- (u, u+v)-construction [i] based on
- appending kth column [i] based on linear OOA(232, 78, F2, 7, 8) (dual of [(78, 7), 514, 9]-NRT-code), using
- net defined by OOA [i] based on linear OOA(232, 78, F2, 8, 8) (dual of [(78, 8), 592, 9]-NRT-code), using
- digital (168, 185, 1048575)-net over F2, using
- net defined by OOA [i] based on linear OOA(2185, 1048575, F2, 17, 17) (dual of [(1048575, 17), 17825590, 18]-NRT-code), using
- OOA 8-folding and stacking with additional row [i] based on linear OA(2185, 8388601, F2, 17) (dual of [8388601, 8388416, 18]-code), using
- discarding factors / shortening the dual code based on linear OA(2185, large, F2, 17) (dual of [large, large−185, 18]-code), using
- the expurgated narrow-sense BCH-code C(I) with length 8388609 | 246−1, defining interval I = [0,8], and minimum distance d ≥ |{−8,−7,…,8}|+1 = 18 (BCH-bound) [i]
- discarding factors / shortening the dual code based on linear OA(2185, large, F2, 17) (dual of [large, large−185, 18]-code), using
- OOA 8-folding and stacking with additional row [i] based on linear OA(2185, 8388601, F2, 17) (dual of [8388601, 8388416, 18]-code), using
- net defined by OOA [i] based on linear OOA(2185, 1048575, F2, 17, 17) (dual of [(1048575, 17), 17825590, 18]-NRT-code), using
- digital (24, 32, 78)-net over F2, 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 (202, 218, 1048653)-net over F2 | [i] | Net Duplication | |
| 2 | Digital (203, 219, 1048653)-net over F2 | [i] | ||