Information on Result #1215235
Digital (100, 112, 2798932)-net over F8, using (u, u+v)-construction based on
- digital (16, 22, 2732)-net over F8, using
- net defined by OOA [i] based on linear OOA(822, 2732, F8, 6, 6) (dual of [(2732, 6), 16370, 7]-NRT-code), using
- OA 3-folding and stacking [i] based on linear OA(822, 8196, F8, 6) (dual of [8196, 8174, 7]-code), using
- trace code [i] based on linear OA(6411, 4098, F64, 6) (dual of [4098, 4087, 7]-code), using
- construction X applied to Ce(5) ⊂ Ce(4) [i] based on
- linear OA(6411, 4096, F64, 6) (dual of [4096, 4085, 7]-code), using an extension Ce(5) of the primitive narrow-sense BCH-code C(I) with length 4095 = 642−1, defining interval I = [1,5], and designed minimum distance d ≥ |I|+1 = 6 [i]
- linear OA(649, 4096, F64, 5) (dual of [4096, 4087, 6]-code), using an extension Ce(4) of the primitive narrow-sense BCH-code C(I) with length 4095 = 642−1, defining interval I = [1,4], and designed minimum distance d ≥ |I|+1 = 5 [i]
- linear OA(640, 2, F64, 0) (dual of [2, 2, 1]-code), using
- discarding factors / shortening the dual code based on linear OA(640, s, F64, 0) (dual of [s, s, 1]-code) for arbitrarily large s, using
- construction X applied to Ce(5) ⊂ Ce(4) [i] based on
- trace code [i] based on linear OA(6411, 4098, F64, 6) (dual of [4098, 4087, 7]-code), using
- OA 3-folding and stacking [i] based on linear OA(822, 8196, F8, 6) (dual of [8196, 8174, 7]-code), using
- net defined by OOA [i] based on linear OOA(822, 2732, F8, 6, 6) (dual of [(2732, 6), 16370, 7]-NRT-code), 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 (101, 113, 2798932)-net over F8 | [i] | Net Duplication | |