Best Known (119−22, 119, s)-Nets in Base 8
(119−22, 119, 23833)-Net over F8 — Constructive and digital
Digital (97, 119, 23833)-net over F8, using
- 81 times duplication [i] based on digital (96, 118, 23833)-net over F8, using
- net defined by OOA [i] based on linear OOA(8118, 23833, F8, 22, 22) (dual of [(23833, 22), 524208, 23]-NRT-code), using
- OA 11-folding and stacking [i] based on linear OA(8118, 262163, F8, 22) (dual of [262163, 262045, 23]-code), using
- discarding factors / shortening the dual code based on linear OA(8118, 262165, F8, 22) (dual of [262165, 262047, 23]-code), using
- construction X applied to Ce(21) ⊂ Ce(18) [i] based on
- 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(897, 262144, F8, 19) (dual of [262144, 262047, 20]-code), using an extension Ce(18) of the primitive narrow-sense BCH-code C(I) with length 262143 = 86−1, defining interval I = [1,18], and designed minimum distance d ≥ |I|+1 = 19 [i]
- linear OA(83, 21, F8, 2) (dual of [21, 18, 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(21) ⊂ Ce(18) [i] based on
- discarding factors / shortening the dual code based on linear OA(8118, 262165, F8, 22) (dual of [262165, 262047, 23]-code), using
- OA 11-folding and stacking [i] based on linear OA(8118, 262163, F8, 22) (dual of [262163, 262045, 23]-code), using
- net defined by OOA [i] based on linear OOA(8118, 23833, F8, 22, 22) (dual of [(23833, 22), 524208, 23]-NRT-code), using
(119−22, 119, 252591)-Net over F8 — Digital
Digital (97, 119, 252591)-net over F8, using
- embedding of OOA with Gilbert–Varšamov bound [i] based on linear OA(8119, 252591, F8, 22) (dual of [252591, 252472, 23]-code), using
- discarding factors / shortening the dual code based on linear OA(8119, 262172, F8, 22) (dual of [262172, 262053, 23]-code), using
- construction X applied to Ce(21) ⊂ Ce(17) [i] based on
- 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(891, 262144, F8, 18) (dual of [262144, 262053, 19]-code), using an extension Ce(17) of the primitive narrow-sense BCH-code C(I) with length 262143 = 86−1, defining interval I = [1,17], and designed minimum distance d ≥ |I|+1 = 18 [i]
- linear OA(84, 28, F8, 3) (dual of [28, 24, 4]-code or 28-cap in PG(3,8)), using
- construction X applied to Ce(21) ⊂ Ce(17) [i] based on
- discarding factors / shortening the dual code based on linear OA(8119, 262172, F8, 22) (dual of [262172, 262053, 23]-code), using
(119−22, 119, large)-Net in Base 8 — Upper bound on s
There is no (97, 119, large)-net in base 8, because
- 20 times m-reduction [i] would yield (97, 99, large)-net in base 8, but