Best Known (138−29, 138, s)-Nets in Base 8
(138−29, 138, 2343)-Net over F8 — Constructive and digital
Digital (109, 138, 2343)-net over F8, using
- 82 times duplication [i] based on digital (107, 136, 2343)-net over F8, using
- net defined by OOA [i] based on linear OOA(8136, 2343, F8, 29, 29) (dual of [(2343, 29), 67811, 30]-NRT-code), using
- OOA 14-folding and stacking with additional row [i] based on linear OA(8136, 32803, F8, 29) (dual of [32803, 32667, 30]-code), using
- discarding factors / shortening the dual code based on linear OA(8136, 32807, F8, 29) (dual of [32807, 32671, 30]-code), using
- construction X applied to Ce(28) ⊂ Ce(21) [i] based on
- linear OA(8126, 32768, F8, 29) (dual of [32768, 32642, 30]-code), using an extension Ce(28) of the primitive narrow-sense BCH-code C(I) with length 32767 = 85−1, defining interval I = [1,28], and designed minimum distance d ≥ |I|+1 = 29 [i]
- linear OA(896, 32768, F8, 22) (dual of [32768, 32672, 23]-code), using an extension Ce(21) of the primitive narrow-sense BCH-code C(I) with length 32767 = 85−1, defining interval I = [1,21], and designed minimum distance d ≥ |I|+1 = 22 [i]
- linear OA(810, 39, F8, 6) (dual of [39, 29, 7]-code), using
- construction X applied to Ce(28) ⊂ Ce(21) [i] based on
- discarding factors / shortening the dual code based on linear OA(8136, 32807, F8, 29) (dual of [32807, 32671, 30]-code), using
- OOA 14-folding and stacking with additional row [i] based on linear OA(8136, 32803, F8, 29) (dual of [32803, 32667, 30]-code), using
- net defined by OOA [i] based on linear OOA(8136, 2343, F8, 29, 29) (dual of [(2343, 29), 67811, 30]-NRT-code), using
(138−29, 138, 45602)-Net over F8 — Digital
Digital (109, 138, 45602)-net over F8, using
(138−29, 138, large)-Net in Base 8 — Upper bound on s
There is no (109, 138, large)-net in base 8, because
- 27 times m-reduction [i] would yield (109, 111, large)-net in base 8, but