Information on Result #1226776
Digital (32, 40, 2228226)-net over F64, using (u, u+v)-construction based on
- digital (7, 11, 131076)-net over F64, using
- net defined by OOA [i] based on linear OOA(6411, 131076, F64, 4, 4) (dual of [(131076, 4), 524293, 5]-NRT-code), using
- appending kth column [i] based on linear OOA(6411, 131076, F64, 3, 4) (dual of [(131076, 3), 393217, 5]-NRT-code), using
- OA 2-folding and stacking [i] based on linear OA(6411, 262152, F64, 4) (dual of [262152, 262141, 5]-code), using
- construction X4 applied to Ce(3) ⊂ Ce(1) [i] based on
- linear OA(6410, 262144, F64, 4) (dual of [262144, 262134, 5]-code), using an extension Ce(3) of the primitive narrow-sense BCH-code C(I) with length 262143 = 643−1, defining interval I = [1,3], and designed minimum distance d ≥ |I|+1 = 4 [i]
- linear OA(644, 262144, F64, 2) (dual of [262144, 262140, 3]-code), using an extension Ce(1) of the primitive narrow-sense BCH-code C(I) with length 262143 = 643−1, defining interval I = [1,1], and designed minimum distance d ≥ |I|+1 = 2 [i]
- linear OA(647, 8, F64, 7) (dual of [8, 1, 8]-code or 8-arc in PG(6,64)), using
- dual of repetition code with length 8 [i]
- linear OA(641, 8, F64, 1) (dual of [8, 7, 2]-code), using
- discarding factors / shortening the dual code based on linear OA(641, 64, F64, 1) (dual of [64, 63, 2]-code), using
- Reed–Solomon code RS(63,64) [i]
- discarding factors / shortening the dual code based on linear OA(641, 64, F64, 1) (dual of [64, 63, 2]-code), using
- construction X4 applied to Ce(3) ⊂ Ce(1) [i] based on
- OA 2-folding and stacking [i] based on linear OA(6411, 262152, F64, 4) (dual of [262152, 262141, 5]-code), using
- appending kth column [i] based on linear OOA(6411, 131076, F64, 3, 4) (dual of [(131076, 3), 393217, 5]-NRT-code), using
- net defined by OOA [i] based on linear OOA(6411, 131076, F64, 4, 4) (dual of [(131076, 4), 524293, 5]-NRT-code), using
- digital (21, 29, 2097150)-net over F64, using
- net defined by OOA [i] based on linear OOA(6429, 2097150, F64, 8, 8) (dual of [(2097150, 8), 16777171, 9]-NRT-code), using
- OA 4-folding and stacking [i] based on linear OA(6429, 8388600, F64, 8) (dual of [8388600, 8388571, 9]-code), using
- discarding factors / shortening the dual code based on linear OA(6429, large, F64, 8) (dual of [large, large−29, 9]-code), using
- the primitive expurgated narrow-sense BCH-code C(I) with length 16777215 = 644−1, defining interval I = [0,7], and designed minimum distance d ≥ |I|+1 = 9 [i]
- discarding factors / shortening the dual code based on linear OA(6429, large, F64, 8) (dual of [large, large−29, 9]-code), using
- OA 4-folding and stacking [i] based on linear OA(6429, 8388600, F64, 8) (dual of [8388600, 8388571, 9]-code), using
- net defined by OOA [i] based on linear OOA(6429, 2097150, F64, 8, 8) (dual of [(2097150, 8), 16777171, 9]-NRT-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 (45, 53, 4456452)-net over F64 | [i] | (u, u+v)-Construction for Nets | |
| 2 | (40, 48, 2228226)-net in base 32 | [i] | Base Change | |