Information on Result #1215467
Digital (136, 152, 2099199)-net over F8, using (u, u+v)-construction based on
- digital (22, 30, 2049)-net over F8, using
- net defined by OOA [i] based on linear OOA(830, 2049, F8, 8, 8) (dual of [(2049, 8), 16362, 9]-NRT-code), using
- OA 4-folding and stacking [i] based on linear OA(830, 8196, F8, 8) (dual of [8196, 8166, 9]-code), using
- trace code [i] based on linear OA(6415, 4098, F64, 8) (dual of [4098, 4083, 9]-code), using
- construction X applied to Ce(7) ⊂ Ce(6) [i] based on
- linear OA(6415, 4096, F64, 8) (dual of [4096, 4081, 9]-code), using an extension Ce(7) of the primitive narrow-sense BCH-code C(I) with length 4095 = 642−1, defining interval I = [1,7], and designed minimum distance d ≥ |I|+1 = 8 [i]
- linear OA(6413, 4096, F64, 7) (dual of [4096, 4083, 8]-code), using an extension Ce(6) of the primitive narrow-sense BCH-code C(I) with length 4095 = 642−1, defining interval I = [1,6], and designed minimum distance d ≥ |I|+1 = 7 [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(7) ⊂ Ce(6) [i] based on
- trace code [i] based on linear OA(6415, 4098, F64, 8) (dual of [4098, 4083, 9]-code), using
- OA 4-folding and stacking [i] based on linear OA(830, 8196, F8, 8) (dual of [8196, 8166, 9]-code), using
- net defined by OOA [i] based on linear OOA(830, 2049, F8, 8, 8) (dual of [(2049, 8), 16362, 9]-NRT-code), using
- digital (106, 122, 2097150)-net over F8, using
- net defined by OOA [i] based on linear OOA(8122, 2097150, F8, 18, 16) (dual of [(2097150, 18), 37748578, 17]-NRT-code), using
- OOA 4-folding and stacking with additional row [i] based on linear OOA(8122, 8388601, F8, 2, 16) (dual of [(8388601, 2), 16777080, 17]-NRT-code), using
- discarding factors / shortening the dual code based on linear OOA(8122, 8388602, F8, 2, 16) (dual of [(8388602, 2), 16777082, 17]-NRT-code), using
- trace code [i] based on linear OOA(6461, 4194301, F64, 2, 16) (dual of [(4194301, 2), 8388541, 17]-NRT-code), using
- OOA 2-folding [i] based on linear OA(6461, 8388602, F64, 16) (dual of [8388602, 8388541, 17]-code), using
- discarding factors / shortening the dual code based on linear OA(6461, large, F64, 16) (dual of [large, large−61, 17]-code), using
- the primitive expurgated narrow-sense BCH-code C(I) with length 16777215 = 644−1, defining interval I = [0,15], and designed minimum distance d ≥ |I|+1 = 17 [i]
- discarding factors / shortening the dual code based on linear OA(6461, large, F64, 16) (dual of [large, large−61, 17]-code), using
- OOA 2-folding [i] based on linear OA(6461, 8388602, F64, 16) (dual of [8388602, 8388541, 17]-code), using
- trace code [i] based on linear OOA(6461, 4194301, F64, 2, 16) (dual of [(4194301, 2), 8388541, 17]-NRT-code), using
- discarding factors / shortening the dual code based on linear OOA(8122, 8388602, F8, 2, 16) (dual of [(8388602, 2), 16777082, 17]-NRT-code), using
- OOA 4-folding and stacking with additional row [i] based on linear OOA(8122, 8388601, F8, 2, 16) (dual of [(8388601, 2), 16777080, 17]-NRT-code), using
- net defined by OOA [i] based on linear OOA(8122, 2097150, F8, 18, 16) (dual of [(2097150, 18), 37748578, 17]-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 (137, 153, 2099199)-net over F8 | [i] | Net Duplication | |