Information on Result #1206291
Digital (239, 257, 933094)-net over F2, using (u, u+v)-construction based on
- digital (41, 50, 1027)-net over F2, using
- net defined by OOA [i] based on linear OOA(250, 1027, F2, 9, 9) (dual of [(1027, 9), 9193, 10]-NRT-code), using
- appending kth column [i] based on linear OOA(250, 1027, F2, 8, 9) (dual of [(1027, 8), 8166, 10]-NRT-code), using
- OOA 4-folding and stacking with additional row [i] based on linear OA(250, 4109, F2, 9) (dual of [4109, 4059, 10]-code), using
- construction X applied to Ce(8) ⊂ Ce(6) [i] based on
- linear OA(249, 4096, F2, 9) (dual of [4096, 4047, 10]-code), using an extension Ce(8) of the primitive narrow-sense BCH-code C(I) with length 4095 = 212−1, defining interval I = [1,8], and designed minimum distance d ≥ |I|+1 = 9 [i]
- linear OA(237, 4096, F2, 7) (dual of [4096, 4059, 8]-code), using an extension Ce(6) of the primitive narrow-sense BCH-code C(I) with length 4095 = 212−1, defining interval I = [1,6], and designed minimum distance d ≥ |I|+1 = 7 [i]
- linear OA(21, 13, F2, 1) (dual of [13, 12, 2]-code), using
- discarding factors / shortening the dual code based on linear OA(21, s, F2, 1) (dual of [s, s−1, 2]-code) for arbitrarily large s, using
- construction X applied to Ce(8) ⊂ Ce(6) [i] based on
- OOA 4-folding and stacking with additional row [i] based on linear OA(250, 4109, F2, 9) (dual of [4109, 4059, 10]-code), using
- appending kth column [i] based on linear OOA(250, 1027, F2, 8, 9) (dual of [(1027, 8), 8166, 10]-NRT-code), using
- net defined by OOA [i] based on linear OOA(250, 1027, F2, 9, 9) (dual of [(1027, 9), 9193, 10]-NRT-code), using
- digital (189, 207, 932067)-net over F2, using
- net defined by OOA [i] based on linear OOA(2207, 932067, F2, 18, 18) (dual of [(932067, 18), 16776999, 19]-NRT-code), using
- OA 9-folding and stacking [i] based on linear OA(2207, large, F2, 18) (dual of [large, large−207, 19]-code), using
- the primitive narrow-sense BCH-code C(I) with length 8388607 = 223−1, defining interval I = [1,18], and designed minimum distance d ≥ |I|+1 = 19 [i]
- OA 9-folding and stacking [i] based on linear OA(2207, large, F2, 18) (dual of [large, large−207, 19]-code), using
- net defined by OOA [i] based on linear OOA(2207, 932067, F2, 18, 18) (dual of [(932067, 18), 16776999, 19]-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 (240, 258, 933094)-net over F2 | [i] | Net Duplication | |
| 2 | Digital (241, 259, 933094)-net over F2 | [i] | ||