Best Known (17−5, 17, s)-Nets in Base 8
(17−5, 17, 4105)-Net over F8 — Constructive and digital
Digital (12, 17, 4105)-net over F8, using
- net defined by OOA [i] based on linear OOA(817, 4105, F8, 6, 5) (dual of [(4105, 6), 24613, 6]-NRT-code), using
- OOA stacking with additional row [i] based on linear OOA(817, 4106, F8, 2, 5) (dual of [(4106, 2), 8195, 6]-NRT-code), using
- (u, u+v)-construction [i] based on
- linear OOA(83, 73, F8, 2, 2) (dual of [(73, 2), 143, 3]-NRT-code), using
- appending kth column [i] based on linear OA(83, 73, F8, 2) (dual of [73, 70, 3]-code), using
- Hamming code H(3,8) [i]
- appending kth column [i] based on linear OA(83, 73, F8, 2) (dual of [73, 70, 3]-code), using
- linear OOA(814, 4033, F8, 2, 5) (dual of [(4033, 2), 8052, 6]-NRT-code), using
- OOA 2-folding [i] based on linear OA(814, 8066, F8, 5) (dual of [8066, 8052, 6]-code), using
- trace code [i] based on linear OA(647, 4033, F64, 5) (dual of [4033, 4026, 6]-code), using
- OOA 2-folding [i] based on linear OA(814, 8066, F8, 5) (dual of [8066, 8052, 6]-code), using
- linear OOA(83, 73, F8, 2, 2) (dual of [(73, 2), 143, 3]-NRT-code), using
- (u, u+v)-construction [i] based on
- OOA stacking with additional row [i] based on linear OOA(817, 4106, F8, 2, 5) (dual of [(4106, 2), 8195, 6]-NRT-code), using
(17−5, 17, 8128)-Net in Base 8 — Constructive
(12, 17, 8128)-net in base 8, using
- net defined by OOA [i] based on OOA(817, 8128, S8, 5, 5), using
- OOA 2-folding and stacking with additional row [i] based on OA(817, 16257, S8, 5), using
- discarding parts of the base [i] based on linear OA(1287, 16257, F128, 5) (dual of [16257, 16250, 6]-code), using
- OOA 2-folding and stacking with additional row [i] based on OA(817, 16257, S8, 5), using
(17−5, 17, 8139)-Net over F8 — Digital
Digital (12, 17, 8139)-net over F8, using
- embedding of OOA with Gilbert–Varšamov bound [i] based on linear OA(817, 8139, F8, 5) (dual of [8139, 8122, 6]-code), using
- (u, u+v)-construction [i] based on
- linear OA(83, 73, F8, 2) (dual of [73, 70, 3]-code), using
- Hamming code H(3,8) [i]
- linear OA(814, 8066, F8, 5) (dual of [8066, 8052, 6]-code), using
- trace code [i] based on linear OA(647, 4033, F64, 5) (dual of [4033, 4026, 6]-code), using
- linear OA(83, 73, F8, 2) (dual of [73, 70, 3]-code), using
- (u, u+v)-construction [i] based on
(17−5, 17, 3389508)-Net in Base 8 — Upper bound on s
There is no (12, 17, 3389509)-net in base 8, because
- 1 times m-reduction [i] would yield (12, 16, 3389509)-net in base 8, but
- the generalized Rao bound for nets shows that 8m ≥ 281 475026 392582 > 816 [i]