Best Known (71, 71+12, s)-Nets in Base 8
(71, 71+12, 1398100)-Net over F8 — Constructive and digital
Digital (71, 83, 1398100)-net over F8, using
- 82 times duplication [i] based on digital (69, 81, 1398100)-net over F8, using
- net defined by OOA [i] based on linear OOA(881, 1398100, F8, 12, 12) (dual of [(1398100, 12), 16777119, 13]-NRT-code), using
- OA 6-folding and stacking [i] based on linear OA(881, 8388600, F8, 12) (dual of [8388600, 8388519, 13]-code), using
- discarding factors / shortening the dual code based on linear OA(881, large, F8, 12) (dual of [large, large−81, 13]-code), using
- the primitive expurgated narrow-sense BCH-code C(I) with length 16777215 = 88−1, defining interval I = [0,11], and designed minimum distance d ≥ |I|+1 = 13 [i]
- discarding factors / shortening the dual code based on linear OA(881, large, F8, 12) (dual of [large, large−81, 13]-code), using
- OA 6-folding and stacking [i] based on linear OA(881, 8388600, F8, 12) (dual of [8388600, 8388519, 13]-code), using
- net defined by OOA [i] based on linear OOA(881, 1398100, F8, 12, 12) (dual of [(1398100, 12), 16777119, 13]-NRT-code), using
(71, 71+12, large)-Net over F8 — Digital
Digital (71, 83, large)-net over F8, using
- 82 times duplication [i] based on digital (69, 81, large)-net over F8, using
- embedding of OOA with Gilbert–VarÅ¡amov bound [i] based on linear OA(881, large, F8, 12) (dual of [large, large−81, 13]-code), using
- the primitive expurgated narrow-sense BCH-code C(I) with length 16777215 = 88−1, defining interval I = [0,11], and designed minimum distance d ≥ |I|+1 = 13 [i]
- embedding of OOA with Gilbert–VarÅ¡amov bound [i] based on linear OA(881, large, F8, 12) (dual of [large, large−81, 13]-code), using
(71, 71+12, large)-Net in Base 8 — Upper bound on s
There is no (71, 83, large)-net in base 8, because
- 10 times m-reduction [i] would yield (71, 73, large)-net in base 8, but