Information on Result #1840475
(51, 72, 1638)-net in base 16, using net defined by OOA based on OOA(1672, 1638, S16, 21, 21), using
- OOA 10-folding and stacking with additional row [i] based on OA(1672, 16381, S16, 21), using
- discarding factors based on OA(1672, 16386, S16, 21), using
- discarding parts of the base [i] based on linear OA(12841, 16386, F128, 21) (dual of [16386, 16345, 22]-code), using
- construction X applied to Ce(20) ⊂ Ce(19) [i] based on
- linear OA(12841, 16384, F128, 21) (dual of [16384, 16343, 22]-code), using an extension Ce(20) of the primitive narrow-sense BCH-code C(I) with length 16383 = 1282−1, defining interval I = [1,20], and designed minimum distance d ≥ |I|+1 = 21 [i]
- linear OA(12839, 16384, F128, 20) (dual of [16384, 16345, 21]-code), using an extension Ce(19) of the primitive narrow-sense BCH-code C(I) with length 16383 = 1282−1, defining interval I = [1,19], and designed minimum distance d ≥ |I|+1 = 20 [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(20) ⊂ Ce(19) [i] based on
- discarding parts of the base [i] based on linear OA(12841, 16386, F128, 21) (dual of [16386, 16345, 22]-code), using
- discarding factors based on OA(1672, 16386, S16, 21), 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 | (52, 73, 1638)-net in base 16 | [i] | Net Duplication | |
| 2 | (53, 74, 1638)-net in base 16 | [i] | ||