Information on Result #3183282
Digital (138, 154, 65538)-net over F2, using t-expansion based on digital (137, 154, 65538)-net over F2, using
- net defined by OOA [i] based on linear OOA(2154, 65538, F2, 17, 17) (dual of [(65538, 17), 1113992, 18]-NRT-code), using
- OOA 8-folding and stacking with additional row [i] based on linear OA(2154, 524305, F2, 17) (dual of [524305, 524151, 18]-code), using
- discarding factors / shortening the dual code based on linear OA(2154, 524308, F2, 17) (dual of [524308, 524154, 18]-code), using
- construction X applied to Ce(16) ⊂ Ce(14) [i] based on
- linear OA(2153, 524288, F2, 17) (dual of [524288, 524135, 18]-code), using an extension Ce(16) of the primitive narrow-sense BCH-code C(I) with length 524287 = 219−1, defining interval I = [1,16], and designed minimum distance d ≥ |I|+1 = 17 [i]
- linear OA(2134, 524288, F2, 15) (dual of [524288, 524154, 16]-code), using an extension Ce(14) of the primitive narrow-sense BCH-code C(I) with length 524287 = 219−1, defining interval I = [1,14], and designed minimum distance d ≥ |I|+1 = 15 [i]
- linear OA(21, 20, F2, 1) (dual of [20, 19, 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(16) ⊂ Ce(14) [i] based on
- discarding factors / shortening the dual code based on linear OA(2154, 524308, F2, 17) (dual of [524308, 524154, 18]-code), using
- OOA 8-folding and stacking with additional row [i] based on linear OA(2154, 524305, F2, 17) (dual of [524305, 524151, 18]-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 (139, 155, 65538)-net over F2 | [i] | Net Duplication | |
| 2 | Digital (140, 156, 65538)-net over F2 | [i] | ||