Best Known (164−29, 164, s)-Nets in Base 8
(164−29, 164, 18728)-Net over F8 — Constructive and digital
Digital (135, 164, 18728)-net over F8, using
- net defined by OOA [i] based on linear OOA(8164, 18728, F8, 29, 29) (dual of [(18728, 29), 542948, 30]-NRT-code), using
- OOA 14-folding and stacking with additional row [i] based on linear OA(8164, 262193, F8, 29) (dual of [262193, 262029, 30]-code), using
- discarding factors / shortening the dual code based on linear OA(8164, 262199, F8, 29) (dual of [262199, 262035, 30]-code), using
- construction X applied to Ce(28) ⊂ Ce(20) [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(8109, 262144, F8, 21) (dual of [262144, 262035, 22]-code), using an extension Ce(20) of the primitive narrow-sense BCH-code C(I) with length 262143 = 86−1, defining interval I = [1,20], and designed minimum distance d ≥ |I|+1 = 21 [i]
- linear OA(813, 55, F8, 7) (dual of [55, 42, 8]-code), using
- discarding factors / shortening the dual code based on linear OA(813, 63, F8, 7) (dual of [63, 50, 8]-code), using
- the primitive expurgated narrow-sense BCH-code C(I) with length 63 = 82−1, defining interval I = [0,6], and designed minimum distance d ≥ |I|+1 = 8 [i]
- discarding factors / shortening the dual code based on linear OA(813, 63, F8, 7) (dual of [63, 50, 8]-code), using
- construction X applied to Ce(28) ⊂ Ce(20) [i] based on
- discarding factors / shortening the dual code based on linear OA(8164, 262199, F8, 29) (dual of [262199, 262035, 30]-code), using
- OOA 14-folding and stacking with additional row [i] based on linear OA(8164, 262193, F8, 29) (dual of [262193, 262029, 30]-code), using
(164−29, 164, 314379)-Net over F8 — Digital
Digital (135, 164, 314379)-net over F8, using
(164−29, 164, large)-Net in Base 8 — Upper bound on s
There is no (135, 164, large)-net in base 8, because
- 27 times m-reduction [i] would yield (135, 137, large)-net in base 8, but