Best Known (125, 125+34, s)-Nets in Base 8
(125, 125+34, 1930)-Net over F8 — Constructive and digital
Digital (125, 159, 1930)-net over F8, using
- 81 times duplication [i] based on digital (124, 158, 1930)-net over F8, using
- net defined by OOA [i] based on linear OOA(8158, 1930, F8, 34, 34) (dual of [(1930, 34), 65462, 35]-NRT-code), using
- OA 17-folding and stacking [i] based on linear OA(8158, 32810, F8, 34) (dual of [32810, 32652, 35]-code), using
- 1 times code embedding in larger space [i] based on linear OA(8157, 32809, F8, 34) (dual of [32809, 32652, 35]-code), using
- construction X applied to Ce(33) ⊂ Ce(26) [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(8116, 32768, F8, 27) (dual of [32768, 32652, 28]-code), using an extension Ce(26) of the primitive narrow-sense BCH-code C(I) with length 32767 = 85−1, defining interval I = [1,26], and designed minimum distance d ≥ |I|+1 = 27 [i]
- linear OA(811, 41, F8, 6) (dual of [41, 30, 7]-code), using
- discarding factors / shortening the dual code based on linear OA(811, 63, F8, 6) (dual of [63, 52, 7]-code), using
- the primitive expurgated narrow-sense BCH-code C(I) with length 63 = 82−1, defining interval I = [0,5], and designed minimum distance d ≥ |I|+1 = 7 [i]
- discarding factors / shortening the dual code based on linear OA(811, 63, F8, 6) (dual of [63, 52, 7]-code), using
- construction X applied to Ce(33) ⊂ Ce(26) [i] based on
- 1 times code embedding in larger space [i] based on linear OA(8157, 32809, F8, 34) (dual of [32809, 32652, 35]-code), using
- OA 17-folding and stacking [i] based on linear OA(8158, 32810, F8, 34) (dual of [32810, 32652, 35]-code), using
- net defined by OOA [i] based on linear OOA(8158, 1930, F8, 34, 34) (dual of [(1930, 34), 65462, 35]-NRT-code), using
(125, 125+34, 42235)-Net over F8 — Digital
Digital (125, 159, 42235)-net over F8, using
(125, 125+34, large)-Net in Base 8 — Upper bound on s
There is no (125, 159, large)-net in base 8, because
- 32 times m-reduction [i] would yield (125, 127, large)-net in base 8, but