Best Known (129−25, 129, s)-Nets in Base 8
(129−25, 129, 21846)-Net over F8 — Constructive and digital
Digital (104, 129, 21846)-net over F8, using
- net defined by OOA [i] based on linear OOA(8129, 21846, F8, 25, 25) (dual of [(21846, 25), 546021, 26]-NRT-code), using
- OOA 12-folding and stacking with additional row [i] based on linear OA(8129, 262153, F8, 25) (dual of [262153, 262024, 26]-code), using
- construction X applied to Ce(24) ⊂ Ce(21) [i] based on
- linear OA(8127, 262144, F8, 25) (dual of [262144, 262017, 26]-code), using an extension Ce(24) of the primitive narrow-sense BCH-code C(I) with length 262143 = 86−1, defining interval I = [1,24], and designed minimum distance d ≥ |I|+1 = 25 [i]
- linear OA(8115, 262144, F8, 22) (dual of [262144, 262029, 23]-code), using an extension Ce(21) of the primitive narrow-sense BCH-code C(I) with length 262143 = 86−1, defining interval I = [1,21], and designed minimum distance d ≥ |I|+1 = 22 [i]
- linear OA(82, 9, F8, 2) (dual of [9, 7, 3]-code or 9-arc in PG(1,8)), using
- extended Reed–Solomon code RSe(7,8) [i]
- Hamming code H(2,8) [i]
- construction X applied to Ce(24) ⊂ Ce(21) [i] based on
- OOA 12-folding and stacking with additional row [i] based on linear OA(8129, 262153, F8, 25) (dual of [262153, 262024, 26]-code), using
(129−25, 129, 142958)-Net over F8 — Digital
Digital (104, 129, 142958)-net over F8, using
- embedding of OOA with Gilbert–Varšamov bound [i] based on linear OA(8129, 142958, F8, 25) (dual of [142958, 142829, 26]-code), using
- discarding factors / shortening the dual code based on linear OA(8129, 262153, F8, 25) (dual of [262153, 262024, 26]-code), using
- construction X applied to Ce(24) ⊂ Ce(21) [i] based on
- linear OA(8127, 262144, F8, 25) (dual of [262144, 262017, 26]-code), using an extension Ce(24) of the primitive narrow-sense BCH-code C(I) with length 262143 = 86−1, defining interval I = [1,24], and designed minimum distance d ≥ |I|+1 = 25 [i]
- linear OA(8115, 262144, F8, 22) (dual of [262144, 262029, 23]-code), using an extension Ce(21) of the primitive narrow-sense BCH-code C(I) with length 262143 = 86−1, defining interval I = [1,21], and designed minimum distance d ≥ |I|+1 = 22 [i]
- linear OA(82, 9, F8, 2) (dual of [9, 7, 3]-code or 9-arc in PG(1,8)), using
- extended Reed–Solomon code RSe(7,8) [i]
- Hamming code H(2,8) [i]
- construction X applied to Ce(24) ⊂ Ce(21) [i] based on
- discarding factors / shortening the dual code based on linear OA(8129, 262153, F8, 25) (dual of [262153, 262024, 26]-code), using
(129−25, 129, large)-Net in Base 8 — Upper bound on s
There is no (104, 129, large)-net in base 8, because
- 23 times m-reduction [i] would yield (104, 106, large)-net in base 8, but