Best Known (168−24, 168, s)-Nets in Base 8
(168−24, 168, 699050)-Net over F8 — Constructive and digital
Digital (144, 168, 699050)-net over F8, using
- net defined by OOA [i] based on linear OOA(8168, 699050, F8, 24, 24) (dual of [(699050, 24), 16777032, 25]-NRT-code), using
- OA 12-folding and stacking [i] based on linear OA(8168, 8388600, F8, 24) (dual of [8388600, 8388432, 25]-code), using
- discarding factors / shortening the dual code 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]
- discarding factors / shortening the dual code based on linear OA(8168, large, F8, 24) (dual of [large, large−168, 25]-code), using
- OA 12-folding and stacking [i] based on linear OA(8168, 8388600, F8, 24) (dual of [8388600, 8388432, 25]-code), using
(168−24, 168, large)-Net over F8 — Digital
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]
(168−24, 168, large)-Net in Base 8 — Upper bound on s
There is no (144, 168, large)-net in base 8, because
- 22 times m-reduction [i] would yield (144, 146, large)-net in base 8, but