Information on Result #1191128
Digital (41, 48, 699260)-net over F8, using net defined by OOA based on linear OOA(848, 699260, F8, 9, 7) (dual of [(699260, 9), 6293292, 8]-NRT-code), using
- OOA stacking with additional row [i] based on linear OOA(848, 699261, F8, 3, 7) (dual of [(699261, 3), 2097735, 8]-NRT-code), using
- (u, u+v)-construction [i] based on
- linear OOA(85, 208, F8, 3, 3) (dual of [(208, 3), 619, 4]-NRT-code), using
- appending kth column [i] based on linear OOA(85, 208, F8, 2, 3) (dual of [(208, 2), 411, 4]-NRT-code), using
- linear OOA(843, 699053, F8, 3, 7) (dual of [(699053, 3), 2097116, 8]-NRT-code), using
- OOA 3-folding [i] based on linear OA(843, 2097159, F8, 7) (dual of [2097159, 2097116, 8]-code), using
- construction X applied to Ce(6) ⊂ Ce(5) [i] based on
- linear OA(843, 2097152, F8, 7) (dual of [2097152, 2097109, 8]-code), using an extension Ce(6) of the primitive narrow-sense BCH-code C(I) with length 2097151 = 87−1, defining interval I = [1,6], and designed minimum distance d ≥ |I|+1 = 7 [i]
- linear OA(836, 2097152, F8, 6) (dual of [2097152, 2097116, 7]-code), using an extension Ce(5) of the primitive narrow-sense BCH-code C(I) with length 2097151 = 87−1, defining interval I = [1,5], and designed minimum distance d ≥ |I|+1 = 6 [i]
- linear OA(80, 7, F8, 0) (dual of [7, 7, 1]-code), using
- discarding factors / shortening the dual code based on linear OA(80, s, F8, 0) (dual of [s, s, 1]-code) for arbitrarily large s, using
- construction X applied to Ce(6) ⊂ Ce(5) [i] based on
- OOA 3-folding [i] based on linear OA(843, 2097159, F8, 7) (dual of [2097159, 2097116, 8]-code), using
- linear OOA(85, 208, F8, 3, 3) (dual of [(208, 3), 619, 4]-NRT-code), using
- (u, u+v)-construction [i] based on
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 (140, 154, 3096002)-net over F8 | [i] | (u, u+v)-Construction for Nets | |
| 2 | Digital (147, 162, 3096002)-net over F8 | [i] | ||