Best Known (119, 147, s)-Nets in Base 8
(119, 147, 18725)-Net over F8 — Constructive and digital
Digital (119, 147, 18725)-net over F8, using
- 82 times duplication [i] based on digital (117, 145, 18725)-net over F8, using
- net defined by OOA [i] based on linear OOA(8145, 18725, F8, 28, 28) (dual of [(18725, 28), 524155, 29]-NRT-code), using
- OA 14-folding and stacking [i] based on linear OA(8145, 262150, F8, 28) (dual of [262150, 262005, 29]-code), using
- construction X applied to Ce(27) ⊂ Ce(26) [i] based on
- linear OA(8145, 262144, F8, 28) (dual of [262144, 261999, 29]-code), using an extension Ce(27) of the primitive narrow-sense BCH-code C(I) with length 262143 = 86−1, defining interval I = [1,27], and designed minimum distance d ≥ |I|+1 = 28 [i]
- 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(80, 6, F8, 0) (dual of [6, 6, 1]-code), using
- discarding factors / shortening the dual code based on linear OA(80, s, F8, 0) (dual of [s, s, 1]-code) with arbitrarily large s, using
- construction X applied to Ce(27) ⊂ Ce(26) [i] based on
- OA 14-folding and stacking [i] based on linear OA(8145, 262150, F8, 28) (dual of [262150, 262005, 29]-code), using
- net defined by OOA [i] based on linear OOA(8145, 18725, F8, 28, 28) (dual of [(18725, 28), 524155, 29]-NRT-code), using
(119, 147, 177564)-Net over F8 — Digital
Digital (119, 147, 177564)-net over F8, using
- embedding of OOA with Gilbert–Varšamov bound [i] based on linear OA(8147, 177564, F8, 28) (dual of [177564, 177417, 29]-code), using
- discarding factors / shortening the dual code based on linear OA(8147, 262159, F8, 28) (dual of [262159, 262012, 29]-code), using
- construction XX applied to Ce(27) ⊂ Ce(25) ⊂ Ce(24) [i] based on
- linear OA(8145, 262144, F8, 28) (dual of [262144, 261999, 29]-code), using an extension Ce(27) of the primitive narrow-sense BCH-code C(I) with length 262143 = 86−1, defining interval I = [1,27], and designed minimum distance d ≥ |I|+1 = 28 [i]
- linear OA(8133, 262144, F8, 26) (dual of [262144, 262011, 27]-code), using an extension Ce(25) of the primitive narrow-sense BCH-code C(I) with length 262143 = 86−1, defining interval I = [1,25], and designed minimum distance d ≥ |I|+1 = 26 [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(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(80, 1, F8, 0) (dual of [1, 1, 1]-code), using
- dual of repetition code with length 1 [i]
- construction XX applied to Ce(27) ⊂ Ce(25) ⊂ Ce(24) [i] based on
- discarding factors / shortening the dual code based on linear OA(8147, 262159, F8, 28) (dual of [262159, 262012, 29]-code), using
(119, 147, large)-Net in Base 8 — Upper bound on s
There is no (119, 147, large)-net in base 8, because
- 26 times m-reduction [i] would yield (119, 121, large)-net in base 8, but