Information on Result #1201636
Digital (21, 40, 456)-net over F64, using net defined by OOA based on linear OOA(6440, 456, F64, 19, 19) (dual of [(456, 19), 8624, 20]-NRT-code), using
- OOA 9-folding and stacking with additional row [i] based on linear OA(6440, 4105, F64, 19) (dual of [4105, 4065, 20]-code), using
- discarding factors / shortening the dual code based on linear OA(6440, 4108, F64, 19) (dual of [4108, 4068, 20]-code), using
- construction X applied to C([0,9]) ⊂ C([0,7]) [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(6429, 4097, F64, 15) (dual of [4097, 4068, 16]-code), using the expurgated narrow-sense BCH-code C(I) with length 4097 | 644−1, defining interval I = [0,7], and minimum distance d ≥ |{−7,−6,…,7}|+1 = 16 (BCH-bound) [i]
- linear OA(643, 11, F64, 3) (dual of [11, 8, 4]-code or 11-arc in PG(2,64) or 11-cap in PG(2,64)), using
- discarding factors / shortening the dual code based on linear OA(643, 64, F64, 3) (dual of [64, 61, 4]-code or 64-arc in PG(2,64) or 64-cap in PG(2,64)), using
- Reed–Solomon code RS(61,64) [i]
- discarding factors / shortening the dual code based on linear OA(643, 64, F64, 3) (dual of [64, 61, 4]-code or 64-arc in PG(2,64) or 64-cap in PG(2,64)), using
- construction X applied to C([0,9]) ⊂ C([0,7]) [i] based on
- discarding factors / shortening the dual code based on linear OA(6440, 4108, F64, 19) (dual of [4108, 4068, 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 (22, 41, 456)-net over F64 | [i] | Net Duplication | |
| 2 | Digital (21, 39, 456)-net over F64 | [i] | m-Reduction | |
| 3 | (29, 48, 456)-net in base 32 | [i] | Base Change | |