Information on Result #1846639
(23, 40, 18824)-net in base 128, using base change based on digital (18, 35, 18824)-net over F256, using
- embedding of OOA with Gilbert–Varšamov bound [i] based on linear OOA(25635, 18824, F256, 3, 17) (dual of [(18824, 3), 56437, 18]-NRT-code), using
- discarding factors / shortening the dual code based on linear OOA(25635, 21848, F256, 3, 17) (dual of [(21848, 3), 65509, 18]-NRT-code), using
- OOA 3-folding [i] based on linear OA(25635, 65544, F256, 17) (dual of [65544, 65509, 18]-code), using
- construction X applied to Ce(16) ⊂ Ce(13) [i] based on
- linear OA(25633, 65536, F256, 17) (dual of [65536, 65503, 18]-code), using an extension Ce(16) of the primitive narrow-sense BCH-code C(I) with length 65535 = 2562−1, defining interval I = [1,16], and designed minimum distance d ≥ |I|+1 = 17 [i]
- linear OA(25627, 65536, F256, 14) (dual of [65536, 65509, 15]-code), using an extension Ce(13) of the primitive narrow-sense BCH-code C(I) with length 65535 = 2562−1, defining interval I = [1,13], and designed minimum distance d ≥ |I|+1 = 14 [i]
- linear OA(2562, 8, F256, 2) (dual of [8, 6, 3]-code or 8-arc in PG(1,256)), using
- discarding factors / shortening the dual code based on linear OA(2562, 256, F256, 2) (dual of [256, 254, 3]-code or 256-arc in PG(1,256)), using
- Reed–Solomon code RS(254,256) [i]
- discarding factors / shortening the dual code based on linear OA(2562, 256, F256, 2) (dual of [256, 254, 3]-code or 256-arc in PG(1,256)), using
- construction X applied to Ce(16) ⊂ Ce(13) [i] based on
- OOA 3-folding [i] based on linear OA(25635, 65544, F256, 17) (dual of [65544, 65509, 18]-code), using
- discarding factors / shortening the dual code based on linear OOA(25635, 21848, F256, 3, 17) (dual of [(21848, 3), 65509, 18]-NRT-code), using
Mode: Arbitrary.
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 | (24, 41, 18824)-net in base 128 | [i] | Net Duplication | |
| 2 | (25, 42, 18824)-net in base 128 | [i] | ||
| 3 | (23, 39, 18824)-net in base 128 | [i] | m-Reduction | |
| 4 | OOA(12840, 18824, S128, 4, 17) | [i] | Extracting Embedded OOA | |