Best Known (43−9, 43, s)-Nets in Base 8
(43−9, 43, 65535)-Net over F8 — Constructive and digital
Digital (34, 43, 65535)-net over F8, using
- net defined by OOA [i] based on linear OOA(843, 65535, F8, 9, 9) (dual of [(65535, 9), 589772, 10]-NRT-code), using
- OOA 4-folding and stacking with additional row [i] based on linear OA(843, 262141, F8, 9) (dual of [262141, 262098, 10]-code), using
- discarding factors / shortening the dual code based on linear OA(843, 262144, F8, 9) (dual of [262144, 262101, 10]-code), using
- an extension Ce(8) of the primitive narrow-sense BCH-code C(I) with length 262143 = 86−1, defining interval I = [1,8], and designed minimum distance d ≥ |I|+1 = 9 [i]
- discarding factors / shortening the dual code based on linear OA(843, 262144, F8, 9) (dual of [262144, 262101, 10]-code), using
- OOA 4-folding and stacking with additional row [i] based on linear OA(843, 262141, F8, 9) (dual of [262141, 262098, 10]-code), using
(43−9, 43, 131072)-Net over F8 — Digital
Digital (34, 43, 131072)-net over F8, using
- embedding of OOA with Gilbert–Varšamov bound [i] based on linear OOA(843, 131072, F8, 2, 9) (dual of [(131072, 2), 262101, 10]-NRT-code), using
- OOA 2-folding [i] based on linear OA(843, 262144, F8, 9) (dual of [262144, 262101, 10]-code), using
- an extension Ce(8) of the primitive narrow-sense BCH-code C(I) with length 262143 = 86−1, defining interval I = [1,8], and designed minimum distance d ≥ |I|+1 = 9 [i]
- OOA 2-folding [i] based on linear OA(843, 262144, F8, 9) (dual of [262144, 262101, 10]-code), using
(43−9, 43, large)-Net in Base 8 — Upper bound on s
There is no (34, 43, large)-net in base 8, because
- 7 times m-reduction [i] would yield (34, 36, large)-net in base 8, but