Best Known (40, 49, s)-Nets in Base 8
(40, 49, 65563)-Net over F8 — Constructive and digital
Digital (40, 49, 65563)-net over F8, using
- (u, u+v)-construction [i] based on
- digital (2, 6, 28)-net over F8, using
- net defined by OOA [i] based on linear OOA(86, 28, F8, 4, 4) (dual of [(28, 4), 106, 5]-NRT-code), using
- appending kth column [i] based on linear OOA(86, 28, F8, 3, 4) (dual of [(28, 3), 78, 5]-NRT-code), using
- OA 2-folding and stacking [i] based on linear OA(86, 56, F8, 4) (dual of [56, 50, 5]-code), using
- 1 times truncation [i] based on linear OA(87, 57, F8, 5) (dual of [57, 50, 6]-code), using
- OA 2-folding and stacking [i] based on linear OA(86, 56, F8, 4) (dual of [56, 50, 5]-code), using
- appending kth column [i] based on linear OOA(86, 28, F8, 3, 4) (dual of [(28, 3), 78, 5]-NRT-code), using
- net defined by OOA [i] based on linear OOA(86, 28, F8, 4, 4) (dual of [(28, 4), 106, 5]-NRT-code), using
- 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
- net defined by OOA [i] based on linear OOA(843, 65535, F8, 9, 9) (dual of [(65535, 9), 589772, 10]-NRT-code), using
- digital (2, 6, 28)-net over F8, using
(40, 49, 262202)-Net over F8 — Digital
Digital (40, 49, 262202)-net over F8, using
- embedding of OOA with Gilbert–Varšamov bound [i] based on linear OA(849, 262202, F8, 9) (dual of [262202, 262153, 10]-code), using
- (u, u+v)-construction [i] based on
- linear OA(86, 58, F8, 4) (dual of [58, 52, 5]-code), using
- a “Gra†code from Grassl’s database [i]
- 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]
- linear OA(86, 58, F8, 4) (dual of [58, 52, 5]-code), using
- (u, u+v)-construction [i] based on
(40, 49, large)-Net in Base 8 — Upper bound on s
There is no (40, 49, large)-net in base 8, because
- 7 times m-reduction [i] would yield (40, 42, large)-net in base 8, but