Best Known (116, 143, s)-Nets in Base 8
(116, 143, 20166)-Net over F8 — Constructive and digital
Digital (116, 143, 20166)-net over F8, using
- 81 times duplication [i] based on digital (115, 142, 20166)-net over F8, using
- net defined by OOA [i] based on linear OOA(8142, 20166, F8, 27, 27) (dual of [(20166, 27), 544340, 28]-NRT-code), using
- OOA 13-folding and stacking with additional row [i] based on linear OA(8142, 262159, F8, 27) (dual of [262159, 262017, 28]-code), using
- discarding factors / shortening the dual code based on linear OA(8142, 262160, F8, 27) (dual of [262160, 262018, 28]-code), using
- construction XX applied to Ce(26) ⊂ Ce(24) ⊂ Ce(22) [i] based on
- linear OA(8139, 262144, F8, 27) (dual of [262144, 262005, 28]-code), using an extension Ce(26) of the primitive narrow-sense BCH-code C(I) with length 262143 = 86−1, defining interval I = [1,26], and designed minimum distance d ≥ |I|+1 = 27 [i]
- 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(8121, 262144, F8, 23) (dual of [262144, 262023, 24]-code), using an extension Ce(22) of the primitive narrow-sense BCH-code C(I) with length 262143 = 86−1, defining interval I = [1,22], and designed minimum distance d ≥ |I|+1 = 23 [i]
- linear OA(81, 14, F8, 1) (dual of [14, 13, 2]-code), using
- discarding factors / shortening the dual code based on linear OA(81, 511, F8, 1) (dual of [511, 510, 2]-code), using
- the primitive expurgated narrow-sense BCH-code C(I) with length 511 = 83−1, defining interval I = [0,0], and designed minimum distance d ≥ |I|+1 = 2 [i]
- discarding factors / shortening the dual code based on linear OA(81, 511, F8, 1) (dual of [511, 510, 2]-code), using
- linear OA(81, 2, F8, 1) (dual of [2, 1, 2]-code), using
- dual of repetition code with length 2 [i]
- construction XX applied to Ce(26) ⊂ Ce(24) ⊂ Ce(22) [i] based on
- discarding factors / shortening the dual code based on linear OA(8142, 262160, F8, 27) (dual of [262160, 262018, 28]-code), using
- OOA 13-folding and stacking with additional row [i] based on linear OA(8142, 262159, F8, 27) (dual of [262159, 262017, 28]-code), using
- net defined by OOA [i] based on linear OOA(8142, 20166, F8, 27, 27) (dual of [(20166, 27), 544340, 28]-NRT-code), using
(116, 143, 195905)-Net over F8 — Digital
Digital (116, 143, 195905)-net over F8, using
- embedding of OOA with Gilbert–Varšamov bound [i] based on linear OA(8143, 195905, F8, 27) (dual of [195905, 195762, 28]-code), using
- discarding factors / shortening the dual code based on linear OA(8143, 262166, F8, 27) (dual of [262166, 262023, 28]-code), using
- construction X applied to Ce(26) ⊂ Ce(22) [i] based on
- linear OA(8139, 262144, F8, 27) (dual of [262144, 262005, 28]-code), using an extension Ce(26) of the primitive narrow-sense BCH-code C(I) with length 262143 = 86−1, defining interval I = [1,26], and designed minimum distance d ≥ |I|+1 = 27 [i]
- linear OA(8121, 262144, F8, 23) (dual of [262144, 262023, 24]-code), using an extension Ce(22) of the primitive narrow-sense BCH-code C(I) with length 262143 = 86−1, defining interval I = [1,22], and designed minimum distance d ≥ |I|+1 = 23 [i]
- linear OA(84, 22, F8, 3) (dual of [22, 18, 4]-code or 22-cap in PG(3,8)), using
- construction X applied to Ce(26) ⊂ Ce(22) [i] based on
- discarding factors / shortening the dual code based on linear OA(8143, 262166, F8, 27) (dual of [262166, 262023, 28]-code), using
(116, 143, large)-Net in Base 8 — Upper bound on s
There is no (116, 143, large)-net in base 8, because
- 25 times m-reduction [i] would yield (116, 118, large)-net in base 8, but