Best Known (157−22, 157, s)-Nets in Base 8
(157−22, 157, 762600)-Net over F8 — Constructive and digital
Digital (135, 157, 762600)-net over F8, using
- 84 times duplication [i] based on digital (131, 153, 762600)-net over F8, using
- net defined by OOA [i] based on linear OOA(8153, 762600, F8, 22, 22) (dual of [(762600, 22), 16777047, 23]-NRT-code), using
- OA 11-folding and stacking [i] based on linear OA(8153, 8388600, F8, 22) (dual of [8388600, 8388447, 23]-code), using
- discarding factors / shortening the dual code based on linear OA(8153, large, F8, 22) (dual of [large, large−153, 23]-code), using
- the primitive expurgated narrow-sense BCH-code C(I) with length 16777215 = 88−1, defining interval I = [0,21], and designed minimum distance d ≥ |I|+1 = 23 [i]
- discarding factors / shortening the dual code based on linear OA(8153, large, F8, 22) (dual of [large, large−153, 23]-code), using
- OA 11-folding and stacking [i] based on linear OA(8153, 8388600, F8, 22) (dual of [8388600, 8388447, 23]-code), using
- net defined by OOA [i] based on linear OOA(8153, 762600, F8, 22, 22) (dual of [(762600, 22), 16777047, 23]-NRT-code), using
(157−22, 157, large)-Net over F8 — Digital
Digital (135, 157, large)-net over F8, using
- 84 times duplication [i] based on digital (131, 153, large)-net over F8, using
- embedding of OOA with Gilbert–VarÅ¡amov bound [i] based on linear OA(8153, large, F8, 22) (dual of [large, large−153, 23]-code), using
- the primitive expurgated narrow-sense BCH-code C(I) with length 16777215 = 88−1, defining interval I = [0,21], and designed minimum distance d ≥ |I|+1 = 23 [i]
- embedding of OOA with Gilbert–VarÅ¡amov bound [i] based on linear OA(8153, large, F8, 22) (dual of [large, large−153, 23]-code), using
(157−22, 157, large)-Net in Base 8 — Upper bound on s
There is no (135, 157, large)-net in base 8, because
- 20 times m-reduction [i] would yield (135, 137, large)-net in base 8, but