Best Known (130−25, 130, s)-Nets in Base 8
(130−25, 130, 21846)-Net over F8 — Constructive and digital
Digital (105, 130, 21846)-net over F8, using
- 81 times duplication [i] based on 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
- net defined by OOA [i] based on linear OOA(8129, 21846, F8, 25, 25) (dual of [(21846, 25), 546021, 26]-NRT-code), using
(130−25, 130, 156487)-Net over F8 — Digital
Digital (105, 130, 156487)-net over F8, using
- embedding of OOA with Gilbert–Varšamov bound [i] based on linear OA(8130, 156487, F8, 25) (dual of [156487, 156357, 26]-code), using
- discarding factors / shortening the dual code based on linear OA(8130, 262159, F8, 25) (dual of [262159, 262029, 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(83, 15, F8, 2) (dual of [15, 12, 3]-code), using
- discarding factors / shortening the dual code based on linear OA(83, 63, F8, 2) (dual of [63, 60, 3]-code), using
- the primitive expurgated narrow-sense BCH-code C(I) with length 63 = 82−1, defining interval I = [0,1], and designed minimum distance d ≥ |I|+1 = 3 [i]
- discarding factors / shortening the dual code based on linear OA(83, 63, F8, 2) (dual of [63, 60, 3]-code), using
- construction X applied to Ce(24) ⊂ Ce(21) [i] based on
- discarding factors / shortening the dual code based on linear OA(8130, 262159, F8, 25) (dual of [262159, 262029, 26]-code), using
(130−25, 130, large)-Net in Base 8 — Upper bound on s
There is no (105, 130, large)-net in base 8, because
- 23 times m-reduction [i] would yield (105, 107, large)-net in base 8, but