Information on Result #3266852
Digital (26, 45, 457)-net over F64, using 643 times duplication based on digital (23, 42, 457)-net over F64, using
- net defined by OOA [i] based on linear OOA(6442, 457, F64, 19, 19) (dual of [(457, 19), 8641, 20]-NRT-code), using
- OOA 9-folding and stacking with additional row [i] based on linear OA(6442, 4114, F64, 19) (dual of [4114, 4072, 20]-code), using
- construction X applied to C([0,9]) ⊂ C([0,6]) [i] based on
- linear OA(6437, 4097, F64, 19) (dual of [4097, 4060, 20]-code), using the expurgated narrow-sense BCH-code C(I) with length 4097 | 644−1, defining interval I = [0,9], and minimum distance d ≥ |{−9,−8,…,9}|+1 = 20 (BCH-bound) [i]
- linear OA(6425, 4097, F64, 13) (dual of [4097, 4072, 14]-code), using the expurgated narrow-sense BCH-code C(I) with length 4097 | 644−1, defining interval I = [0,6], and minimum distance d ≥ |{−6,−5,…,6}|+1 = 14 (BCH-bound) [i]
- linear OA(645, 17, F64, 5) (dual of [17, 12, 6]-code or 17-arc in PG(4,64)), using
- discarding factors / shortening the dual code based on linear OA(645, 64, F64, 5) (dual of [64, 59, 6]-code or 64-arc in PG(4,64)), using
- Reed–Solomon code RS(59,64) [i]
- discarding factors / shortening the dual code based on linear OA(645, 64, F64, 5) (dual of [64, 59, 6]-code or 64-arc in PG(4,64)), using
- construction X applied to C([0,9]) ⊂ C([0,6]) [i] based on
- OOA 9-folding and stacking with additional row [i] based on linear OA(6442, 4114, F64, 19) (dual of [4114, 4072, 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 | (35, 54, 457)-net in base 32 | [i] | Base Change | |