Information on Result #1229985
Digital (131, 143, 5596432)-net over F8, using generalized (u, u+v)-construction based on
- digital (8, 12, 4032)-net over F8, using
- net defined by OOA [i] based on linear OOA(812, 4032, F8, 4, 4) (dual of [(4032, 4), 16116, 5]-NRT-code), using
- appending kth column [i] based on linear OOA(812, 4032, F8, 3, 4) (dual of [(4032, 3), 12084, 5]-NRT-code), using
- OA 2-folding and stacking [i] based on linear OA(812, 8064, F8, 4) (dual of [8064, 8052, 5]-code), using
- trace code [i] based on linear OA(646, 4032, F64, 4) (dual of [4032, 4026, 5]-code), using
- 1 times truncation [i] based on linear OA(647, 4033, F64, 5) (dual of [4033, 4026, 6]-code), using
- trace code [i] based on linear OA(646, 4032, F64, 4) (dual of [4032, 4026, 5]-code), using
- OA 2-folding and stacking [i] based on linear OA(812, 8064, F8, 4) (dual of [8064, 8052, 5]-code), using
- appending kth column [i] based on linear OOA(812, 4032, F8, 3, 4) (dual of [(4032, 3), 12084, 5]-NRT-code), using
- net defined by OOA [i] based on linear OOA(812, 4032, F8, 4, 4) (dual of [(4032, 4), 16116, 5]-NRT-code), using
- digital (35, 41, 2796200)-net over F8, using
- s-reduction based on digital (35, 41, 2796201)-net over F8, using
- net defined by OOA [i] based on linear OOA(841, 2796201, F8, 6, 6) (dual of [(2796201, 6), 16777165, 7]-NRT-code), using
- OA 3-folding and stacking [i] based on linear OA(841, large, F8, 6) (dual of [large, large−41, 7]-code), using
- the primitive expurgated narrow-sense BCH-code C(I) with length 16777215 = 88−1, defining interval I = [0,5], and designed minimum distance d ≥ |I|+1 = 7 [i]
- OA 3-folding and stacking [i] based on linear OA(841, large, F8, 6) (dual of [large, large−41, 7]-code), using
- net defined by OOA [i] based on linear OOA(841, 2796201, F8, 6, 6) (dual of [(2796201, 6), 16777165, 7]-NRT-code), using
- s-reduction based on digital (35, 41, 2796201)-net over F8, using
- digital (78, 90, 2796200)-net over F8, using
- net defined by OOA [i] based on linear OOA(890, 2796200, F8, 14, 12) (dual of [(2796200, 14), 39146710, 13]-NRT-code), using
- OOA 3-folding and stacking with additional row [i] based on linear OOA(890, 8388601, F8, 2, 12) (dual of [(8388601, 2), 16777112, 13]-NRT-code), using
- discarding factors / shortening the dual code based on linear OOA(890, 8388602, F8, 2, 12) (dual of [(8388602, 2), 16777114, 13]-NRT-code), using
- trace code [i] based on linear OOA(6445, 4194301, F64, 2, 12) (dual of [(4194301, 2), 8388557, 13]-NRT-code), using
- OOA 2-folding [i] based on linear OA(6445, 8388602, F64, 12) (dual of [8388602, 8388557, 13]-code), using
- discarding factors / shortening the dual code based on linear OA(6445, large, F64, 12) (dual of [large, large−45, 13]-code), using
- the primitive expurgated narrow-sense BCH-code C(I) with length 16777215 = 644−1, defining interval I = [0,11], and designed minimum distance d ≥ |I|+1 = 13 [i]
- discarding factors / shortening the dual code based on linear OA(6445, large, F64, 12) (dual of [large, large−45, 13]-code), using
- OOA 2-folding [i] based on linear OA(6445, 8388602, F64, 12) (dual of [8388602, 8388557, 13]-code), using
- trace code [i] based on linear OOA(6445, 4194301, F64, 2, 12) (dual of [(4194301, 2), 8388557, 13]-NRT-code), using
- discarding factors / shortening the dual code based on linear OOA(890, 8388602, F8, 2, 12) (dual of [(8388602, 2), 16777114, 13]-NRT-code), using
- OOA 3-folding and stacking with additional row [i] based on linear OOA(890, 8388601, F8, 2, 12) (dual of [(8388601, 2), 16777112, 13]-NRT-code), using
- net defined by OOA [i] based on linear OOA(890, 2796200, F8, 14, 12) (dual of [(2796200, 14), 39146710, 13]-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 (132, 144, 5596432)-net over F8 | [i] | Net Duplication | |