Best Known (47, 47+14, s)-Nets in Base 8
(47, 47+14, 4681)-Net over F8 — Constructive and digital
Digital (47, 61, 4681)-net over F8, using
- net defined by OOA [i] based on linear OOA(861, 4681, F8, 14, 14) (dual of [(4681, 14), 65473, 15]-NRT-code), using
- OA 7-folding and stacking [i] based on linear OA(861, 32767, F8, 14) (dual of [32767, 32706, 15]-code), using
- discarding factors / shortening the dual code based on linear OA(861, 32768, F8, 14) (dual of [32768, 32707, 15]-code), using
- an extension Ce(13) of the primitive narrow-sense BCH-code C(I) with length 32767 = 85−1, defining interval I = [1,13], and designed minimum distance d ≥ |I|+1 = 14 [i]
- discarding factors / shortening the dual code based on linear OA(861, 32768, F8, 14) (dual of [32768, 32707, 15]-code), using
- OA 7-folding and stacking [i] based on linear OA(861, 32767, F8, 14) (dual of [32767, 32706, 15]-code), using
(47, 47+14, 24751)-Net over F8 — Digital
Digital (47, 61, 24751)-net over F8, using
- embedding of OOA with Gilbert–Varšamov bound [i] based on linear OA(861, 24751, F8, 14) (dual of [24751, 24690, 15]-code), using
- discarding factors / shortening the dual code based on linear OA(861, 32768, F8, 14) (dual of [32768, 32707, 15]-code), using
- an extension Ce(13) of the primitive narrow-sense BCH-code C(I) with length 32767 = 85−1, defining interval I = [1,13], and designed minimum distance d ≥ |I|+1 = 14 [i]
- discarding factors / shortening the dual code based on linear OA(861, 32768, F8, 14) (dual of [32768, 32707, 15]-code), using
(47, 47+14, large)-Net in Base 8 — Upper bound on s
There is no (47, 61, large)-net in base 8, because
- 12 times m-reduction [i] would yield (47, 49, large)-net in base 8, but