Best Known (115, 115+34, s)-Nets in Base 8
(115, 115+34, 1928)-Net over F8 — Constructive and digital
Digital (115, 149, 1928)-net over F8, using
- 81 times duplication [i] based on digital (114, 148, 1928)-net over F8, using
- net defined by OOA [i] based on linear OOA(8148, 1928, F8, 34, 34) (dual of [(1928, 34), 65404, 35]-NRT-code), using
- OA 17-folding and stacking [i] based on linear OA(8148, 32776, F8, 34) (dual of [32776, 32628, 35]-code), using
- discarding factors / shortening the dual code based on linear OA(8148, 32777, F8, 34) (dual of [32777, 32629, 35]-code), using
- construction X applied to Ce(33) ⊂ Ce(30) [i] based on
- linear OA(8146, 32768, F8, 34) (dual of [32768, 32622, 35]-code), using an extension Ce(33) of the primitive narrow-sense BCH-code C(I) with length 32767 = 85−1, defining interval I = [1,33], and designed minimum distance d ≥ |I|+1 = 34 [i]
- linear OA(8136, 32768, F8, 31) (dual of [32768, 32632, 32]-code), using an extension Ce(30) of the primitive narrow-sense BCH-code C(I) with length 32767 = 85−1, defining interval I = [1,30], and designed minimum distance d ≥ |I|+1 = 31 [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(33) ⊂ Ce(30) [i] based on
- discarding factors / shortening the dual code based on linear OA(8148, 32777, F8, 34) (dual of [32777, 32629, 35]-code), using
- OA 17-folding and stacking [i] based on linear OA(8148, 32776, F8, 34) (dual of [32776, 32628, 35]-code), using
- net defined by OOA [i] based on linear OOA(8148, 1928, F8, 34, 34) (dual of [(1928, 34), 65404, 35]-NRT-code), using
(115, 115+34, 27432)-Net over F8 — Digital
Digital (115, 149, 27432)-net over F8, using
- embedding of OOA with Gilbert–Varšamov bound [i] based on linear OA(8149, 27432, F8, 34) (dual of [27432, 27283, 35]-code), using
- discarding factors / shortening the dual code based on linear OA(8149, 32781, F8, 34) (dual of [32781, 32632, 35]-code), using
- construction X applied to Ce(33) ⊂ Ce(30) [i] based on
- linear OA(8146, 32768, F8, 34) (dual of [32768, 32622, 35]-code), using an extension Ce(33) of the primitive narrow-sense BCH-code C(I) with length 32767 = 85−1, defining interval I = [1,33], and designed minimum distance d ≥ |I|+1 = 34 [i]
- linear OA(8136, 32768, F8, 31) (dual of [32768, 32632, 32]-code), using an extension Ce(30) of the primitive narrow-sense BCH-code C(I) with length 32767 = 85−1, defining interval I = [1,30], and designed minimum distance d ≥ |I|+1 = 31 [i]
- linear OA(83, 13, F8, 2) (dual of [13, 10, 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(33) ⊂ Ce(30) [i] based on
- discarding factors / shortening the dual code based on linear OA(8149, 32781, F8, 34) (dual of [32781, 32632, 35]-code), using
(115, 115+34, large)-Net in Base 8 — Upper bound on s
There is no (115, 149, large)-net in base 8, because
- 32 times m-reduction [i] would yield (115, 117, large)-net in base 8, but