Best Known (171−22, 171, s)-Nets in Base 8
(171−22, 171, 1525200)-Net over F8 — Constructive and digital
Digital (149, 171, 1525200)-net over F8, using
- 81 times duplication [i] based on digital (148, 170, 1525200)-net over F8, using
- trace code for nets [i] based on digital (63, 85, 762600)-net over F64, using
- net defined by OOA [i] based on linear OOA(6485, 762600, F64, 22, 22) (dual of [(762600, 22), 16777115, 23]-NRT-code), using
- OA 11-folding and stacking [i] based on linear OA(6485, 8388600, F64, 22) (dual of [8388600, 8388515, 23]-code), using
- discarding factors / shortening the dual code based on linear OA(6485, large, F64, 22) (dual of [large, large−85, 23]-code), using
- the primitive expurgated narrow-sense BCH-code C(I) with length 16777215 = 644−1, defining interval I = [0,21], and designed minimum distance d ≥ |I|+1 = 23 [i]
- discarding factors / shortening the dual code based on linear OA(6485, large, F64, 22) (dual of [large, large−85, 23]-code), using
- OA 11-folding and stacking [i] based on linear OA(6485, 8388600, F64, 22) (dual of [8388600, 8388515, 23]-code), using
- net defined by OOA [i] based on linear OOA(6485, 762600, F64, 22, 22) (dual of [(762600, 22), 16777115, 23]-NRT-code), using
- trace code for nets [i] based on digital (63, 85, 762600)-net over F64, using
(171−22, 171, large)-Net over F8 — Digital
Digital (149, 171, large)-net over F8, using
- 83 times duplication [i] based on digital (146, 168, large)-net over F8, using
- t-expansion [i] based on digital (144, 168, large)-net over F8, using
- embedding of OOA with Gilbert–VarÅ¡amov bound [i] based on linear OA(8168, large, F8, 24) (dual of [large, large−168, 25]-code), using
- the primitive narrow-sense BCH-code C(I) with length 16777215 = 88−1, defining interval I = [1,24], and designed minimum distance d ≥ |I|+1 = 25 [i]
- embedding of OOA with Gilbert–VarÅ¡amov bound [i] based on linear OA(8168, large, F8, 24) (dual of [large, large−168, 25]-code), using
- t-expansion [i] based on digital (144, 168, large)-net over F8, using
(171−22, 171, large)-Net in Base 8 — Upper bound on s
There is no (149, 171, large)-net in base 8, because
- 20 times m-reduction [i] would yield (149, 151, large)-net in base 8, but