Best Known (155−29, 155, s)-Nets in Base 8
(155−29, 155, 18726)-Net over F8 — Constructive and digital
Digital (126, 155, 18726)-net over F8, using
- 81 times duplication [i] based on digital (125, 154, 18726)-net over F8, using
- net defined by OOA [i] based on linear OOA(8154, 18726, F8, 29, 29) (dual of [(18726, 29), 542900, 30]-NRT-code), using
- OOA 14-folding and stacking with additional row [i] based on linear OA(8154, 262165, F8, 29) (dual of [262165, 262011, 30]-code), using
- construction X applied to Ce(28) ⊂ Ce(25) [i] based on
- linear OA(8151, 262144, F8, 29) (dual of [262144, 261993, 30]-code), using an extension Ce(28) of the primitive narrow-sense BCH-code C(I) with length 262143 = 86−1, defining interval I = [1,28], and designed minimum distance d ≥ |I|+1 = 29 [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(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(28) ⊂ Ce(25) [i] based on
- OOA 14-folding and stacking with additional row [i] based on linear OA(8154, 262165, F8, 29) (dual of [262165, 262011, 30]-code), using
- net defined by OOA [i] based on linear OOA(8154, 18726, F8, 29, 29) (dual of [(18726, 29), 542900, 30]-NRT-code), using
(155−29, 155, 220920)-Net over F8 — Digital
Digital (126, 155, 220920)-net over F8, using
- embedding of OOA with Gilbert–Varšamov bound [i] based on linear OA(8155, 220920, F8, 29) (dual of [220920, 220765, 30]-code), using
- discarding factors / shortening the dual code based on linear OA(8155, 262172, F8, 29) (dual of [262172, 262017, 30]-code), using
- construction X applied to Ce(28) ⊂ Ce(24) [i] based on
- linear OA(8151, 262144, F8, 29) (dual of [262144, 261993, 30]-code), using an extension Ce(28) of the primitive narrow-sense BCH-code C(I) with length 262143 = 86−1, defining interval I = [1,28], and designed minimum distance d ≥ |I|+1 = 29 [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(84, 28, F8, 3) (dual of [28, 24, 4]-code or 28-cap in PG(3,8)), using
- construction X applied to Ce(28) ⊂ Ce(24) [i] based on
- discarding factors / shortening the dual code based on linear OA(8155, 262172, F8, 29) (dual of [262172, 262017, 30]-code), using
(155−29, 155, large)-Net in Base 8 — Upper bound on s
There is no (126, 155, large)-net in base 8, because
- 27 times m-reduction [i] would yield (126, 128, large)-net in base 8, but