Information on Result #1841871
(57, 69, 4194301)-net in base 128, using net defined by OOA based on OOA(12869, 4194301, S128, 15, 12), using
- OOA 2-folding and stacking with additional row [i] based on OOA(12869, large, S128, 3, 12), using
- discarding parts of the base [i] based on linear OOA(25660, large, F256, 3, 12), using
- generalized (u, u+v)-construction [i] based on
- linear OOA(25610, 2796201, F256, 3, 4) (dual of [(2796201, 3), 8388593, 5]-NRT-code), using
- discarding factors / shortening the dual code based on linear OOA(25610, 4194301, F256, 3, 4) (dual of [(4194301, 3), 12582893, 5]-NRT-code), using
- OA 2-folding and stacking [i] based on linear OA(25610, 8388602, F256, 4) (dual of [8388602, 8388592, 5]-code), using
- discarding factors / shortening the dual code based on linear OA(25610, large, F256, 4) (dual of [large, large−10, 5]-code), using
- the primitive expurgated narrow-sense BCH-code C(I) with length 16777215 = 2563−1, defining interval I = [0,3], and designed minimum distance d ≥ |I|+1 = 5 [i]
- discarding factors / shortening the dual code based on linear OA(25610, large, F256, 4) (dual of [large, large−10, 5]-code), using
- OA 2-folding and stacking [i] based on linear OA(25610, 8388602, F256, 4) (dual of [8388602, 8388592, 5]-code), using
- discarding factors / shortening the dual code based on linear OOA(25610, 4194301, F256, 3, 4) (dual of [(4194301, 3), 12582893, 5]-NRT-code), using
- linear OOA(25616, 2796201, F256, 3, 6) (dual of [(2796201, 3), 8388587, 7]-NRT-code), using
- OOA 3-folding [i] based on linear OA(25616, large, F256, 6) (dual of [large, large−16, 7]-code), using
- the primitive expurgated narrow-sense BCH-code C(I) with length 16777215 = 2563−1, defining interval I = [0,5], and designed minimum distance d ≥ |I|+1 = 7 [i]
- OOA 3-folding [i] based on linear OA(25616, large, F256, 6) (dual of [large, large−16, 7]-code), using
- linear OOA(25634, 2796201, F256, 3, 12) (dual of [(2796201, 3), 8388569, 13]-NRT-code), using
- OOA 3-folding [i] based on linear OA(25634, large, F256, 12) (dual of [large, large−34, 13]-code), using
- the primitive expurgated narrow-sense BCH-code C(I) with length 16777215 = 2563−1, defining interval I = [0,11], and designed minimum distance d ≥ |I|+1 = 13 [i]
- OOA 3-folding [i] based on linear OA(25634, large, F256, 12) (dual of [large, large−34, 13]-code), using
- linear OOA(25610, 2796201, F256, 3, 4) (dual of [(2796201, 3), 8388593, 5]-NRT-code), using
- generalized (u, u+v)-construction [i] based on
- discarding parts of the base [i] based on linear OOA(25660, large, F256, 3, 12), 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 | (58, 70, 4194301)-net in base 128 | [i] | Net Duplication | |
| 2 | (64, 76, 4194558)-net in base 128 | [i] | (u, u+v)-Construction for Nets | |