Best Known (143−20, 143, s)-Nets in Base 8
(143−20, 143, 838860)-Net over F8 — Constructive and digital
Digital (123, 143, 838860)-net over F8, using
- 86 times duplication [i] based on digital (117, 137, 838860)-net over F8, using
- net defined by OOA [i] based on linear OOA(8137, 838860, F8, 20, 20) (dual of [(838860, 20), 16777063, 21]-NRT-code), using
- OA 10-folding and stacking [i] based on linear OA(8137, 8388600, F8, 20) (dual of [8388600, 8388463, 21]-code), using
- discarding factors / shortening the dual code based on linear OA(8137, large, F8, 20) (dual of [large, large−137, 21]-code), using
- the primitive expurgated narrow-sense BCH-code C(I) with length 16777215 = 88−1, defining interval I = [0,19], and designed minimum distance d ≥ |I|+1 = 21 [i]
- discarding factors / shortening the dual code based on linear OA(8137, large, F8, 20) (dual of [large, large−137, 21]-code), using
- OA 10-folding and stacking [i] based on linear OA(8137, 8388600, F8, 20) (dual of [8388600, 8388463, 21]-code), using
- net defined by OOA [i] based on linear OOA(8137, 838860, F8, 20, 20) (dual of [(838860, 20), 16777063, 21]-NRT-code), using
(143−20, 143, large)-Net over F8 — Digital
Digital (123, 143, large)-net over F8, using
- 84 times duplication [i] based on digital (119, 139, large)-net over F8, using
- embedding of OOA with Gilbert–VarÅ¡amov bound [i] based on linear OA(8139, large, F8, 20) (dual of [large, large−139, 21]-code), using
- 2 times code embedding in larger space [i] based on linear OA(8137, large, F8, 20) (dual of [large, large−137, 21]-code), using
- the primitive expurgated narrow-sense BCH-code C(I) with length 16777215 = 88−1, defining interval I = [0,19], and designed minimum distance d ≥ |I|+1 = 21 [i]
- 2 times code embedding in larger space [i] based on linear OA(8137, large, F8, 20) (dual of [large, large−137, 21]-code), using
- embedding of OOA with Gilbert–VarÅ¡amov bound [i] based on linear OA(8139, large, F8, 20) (dual of [large, large−139, 21]-code), using
(143−20, 143, large)-Net in Base 8 — Upper bound on s
There is no (123, 143, large)-net in base 8, because
- 18 times m-reduction [i] would yield (123, 125, large)-net in base 8, but