Information on Result #1840443
(41, 58, 2048)-net in base 16, using net defined by OOA based on OOA(1658, 2048, S16, 17, 17), using
- OOA 8-folding and stacking with additional row [i] based on OA(1658, 16385, S16, 17), using
- discarding factors based on OA(1658, 16386, S16, 17), using
- discarding parts of the base [i] based on linear OA(12833, 16386, F128, 17) (dual of [16386, 16353, 18]-code), using
- construction X applied to Ce(16) ⊂ Ce(15) [i] based on
- linear OA(12833, 16384, F128, 17) (dual of [16384, 16351, 18]-code), using an extension Ce(16) of the primitive narrow-sense BCH-code C(I) with length 16383 = 1282−1, defining interval I = [1,16], and designed minimum distance d ≥ |I|+1 = 17 [i]
- linear OA(12831, 16384, F128, 16) (dual of [16384, 16353, 17]-code), using an extension Ce(15) of the primitive narrow-sense BCH-code C(I) with length 16383 = 1282−1, defining interval I = [1,15], and designed minimum distance d ≥ |I|+1 = 16 [i]
- linear OA(1280, 2, F128, 0) (dual of [2, 2, 1]-code), using
- discarding factors / shortening the dual code based on linear OA(1280, s, F128, 0) (dual of [s, s, 1]-code) for arbitrarily large s, using
- construction X applied to Ce(16) ⊂ Ce(15) [i] based on
- discarding parts of the base [i] based on linear OA(12833, 16386, F128, 17) (dual of [16386, 16353, 18]-code), using
- discarding factors based on OA(1658, 16386, S16, 17), using
Mode: Constructive.
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 | (42, 59, 2048)-net in base 16 | [i] | Net Duplication | |
| 2 | (43, 60, 2048)-net in base 16 | [i] | ||
| 3 | (41, 57, 2048)-net in base 16 | [i] | m-Reduction | |