Information on Result #1201500
Digital (19, 36, 513)-net over F64, using net defined by OOA based on linear OOA(6436, 513, F64, 17, 17) (dual of [(513, 17), 8685, 18]-NRT-code), using
- OOA 8-folding and stacking with additional row [i] based on linear OA(6436, 4105, F64, 17) (dual of [4105, 4069, 18]-code), using
- discarding factors / shortening the dual code based on linear OA(6436, 4108, F64, 17) (dual of [4108, 4072, 18]-code), using
- construction X applied to C([0,8]) ⊂ C([0,6]) [i] based on
- linear OA(6433, 4097, F64, 17) (dual of [4097, 4064, 18]-code), using the expurgated narrow-sense BCH-code C(I) with length 4097 | 644−1, defining interval I = [0,8], and minimum distance d ≥ |{−8,−7,…,8}|+1 = 18 (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(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([0,8]) ⊂ C([0,6]) [i] based on
- discarding factors / shortening the dual code based on linear OA(6436, 4108, F64, 17) (dual of [4108, 4072, 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 (20, 37, 513)-net over F64 | [i] | Net Duplication | |
| 2 | Digital (19, 35, 513)-net over F64 | [i] | m-Reduction | |