Best Known (49, 49+22, s)-Nets in Base 128
(49, 49+22, 190653)-Net over F128 — Constructive and digital
Digital (49, 71, 190653)-net over F128, using
- net defined by OOA [i] based on linear OOA(12871, 190653, F128, 22, 22) (dual of [(190653, 22), 4194295, 23]-NRT-code), using
- OA 11-folding and stacking [i] based on linear OA(12871, 2097183, F128, 22) (dual of [2097183, 2097112, 23]-code), using
- construction X applied to Ce(21) ⊂ Ce(13) [i] based on
- linear OA(12864, 2097152, F128, 22) (dual of [2097152, 2097088, 23]-code), using an extension Ce(21) of the primitive narrow-sense BCH-code C(I) with length 2097151 = 1283−1, defining interval I = [1,21], and designed minimum distance d ≥ |I|+1 = 22 [i]
- linear OA(12840, 2097152, F128, 14) (dual of [2097152, 2097112, 15]-code), using an extension Ce(13) of the primitive narrow-sense BCH-code C(I) with length 2097151 = 1283−1, defining interval I = [1,13], and designed minimum distance d ≥ |I|+1 = 14 [i]
- linear OA(1287, 31, F128, 7) (dual of [31, 24, 8]-code or 31-arc in PG(6,128)), using
- discarding factors / shortening the dual code based on linear OA(1287, 128, F128, 7) (dual of [128, 121, 8]-code or 128-arc in PG(6,128)), using
- Reed–Solomon code RS(121,128) [i]
- discarding factors / shortening the dual code based on linear OA(1287, 128, F128, 7) (dual of [128, 121, 8]-code or 128-arc in PG(6,128)), using
- construction X applied to Ce(21) ⊂ Ce(13) [i] based on
- OA 11-folding and stacking [i] based on linear OA(12871, 2097183, F128, 22) (dual of [2097183, 2097112, 23]-code), using
(49, 49+22, 1551439)-Net over F128 — Digital
Digital (49, 71, 1551439)-net over F128, using
- embedding of OOA with Gilbert–Varšamov bound [i] based on linear OA(12871, 1551439, F128, 22) (dual of [1551439, 1551368, 23]-code), using
- discarding factors / shortening the dual code based on linear OA(12871, 2097183, F128, 22) (dual of [2097183, 2097112, 23]-code), using
- construction X applied to Ce(21) ⊂ Ce(13) [i] based on
- linear OA(12864, 2097152, F128, 22) (dual of [2097152, 2097088, 23]-code), using an extension Ce(21) of the primitive narrow-sense BCH-code C(I) with length 2097151 = 1283−1, defining interval I = [1,21], and designed minimum distance d ≥ |I|+1 = 22 [i]
- linear OA(12840, 2097152, F128, 14) (dual of [2097152, 2097112, 15]-code), using an extension Ce(13) of the primitive narrow-sense BCH-code C(I) with length 2097151 = 1283−1, defining interval I = [1,13], and designed minimum distance d ≥ |I|+1 = 14 [i]
- linear OA(1287, 31, F128, 7) (dual of [31, 24, 8]-code or 31-arc in PG(6,128)), using
- discarding factors / shortening the dual code based on linear OA(1287, 128, F128, 7) (dual of [128, 121, 8]-code or 128-arc in PG(6,128)), using
- Reed–Solomon code RS(121,128) [i]
- discarding factors / shortening the dual code based on linear OA(1287, 128, F128, 7) (dual of [128, 121, 8]-code or 128-arc in PG(6,128)), using
- construction X applied to Ce(21) ⊂ Ce(13) [i] based on
- discarding factors / shortening the dual code based on linear OA(12871, 2097183, F128, 22) (dual of [2097183, 2097112, 23]-code), using
(49, 49+22, large)-Net in Base 128 — Upper bound on s
There is no (49, 71, large)-net in base 128, because
- 20 times m-reduction [i] would yield (49, 51, large)-net in base 128, but