Best Known (9, 9+4, s)-Nets in Base 8
(9, 9+4, 4032)-Net over F8 — Constructive and digital
Digital (9, 13, 4032)-net over F8, using
- 1 times m-reduction [i] based on digital (9, 14, 4032)-net over F8, using
- net defined by OOA [i] based on linear OOA(814, 4032, F8, 5, 5) (dual of [(4032, 5), 20146, 6]-NRT-code), using
- OOA 2-folding and stacking with additional row [i] based on linear OA(814, 8065, F8, 5) (dual of [8065, 8051, 6]-code), using
- discarding factors / shortening the dual code 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
- discarding factors / shortening the dual code based on linear OA(814, 8066, F8, 5) (dual of [8066, 8052, 6]-code), using
- OOA 2-folding and stacking with additional row [i] based on linear OA(814, 8065, F8, 5) (dual of [8065, 8051, 6]-code), using
- net defined by OOA [i] based on linear OOA(814, 4032, F8, 5, 5) (dual of [(4032, 5), 20146, 6]-NRT-code), using
(9, 9+4, 8066)-Net over F8 — Digital
Digital (9, 13, 8066)-net over F8, using
- net defined by OOA [i] based on linear OOA(813, 8066, F8, 4, 4) (dual of [(8066, 4), 32251, 5]-NRT-code), using
- appending kth column [i] based on linear OOA(813, 8066, F8, 3, 4) (dual of [(8066, 3), 24185, 5]-NRT-code), using
- embedding of OOA with Gilbert–Varšamov bound [i] based on linear OA(813, 8066, F8, 4) (dual of [8066, 8053, 5]-code), using
- construction X with Varšamov bound [i] based on
- linear OA(812, 8064, F8, 4) (dual of [8064, 8052, 5]-code), using
- trace code [i] based on linear OA(646, 4032, F64, 4) (dual of [4032, 4026, 5]-code), using
- 1 times truncation [i] based on linear OA(647, 4033, F64, 5) (dual of [4033, 4026, 6]-code), using
- trace code [i] based on linear OA(646, 4032, F64, 4) (dual of [4032, 4026, 5]-code), using
- linear OA(812, 8065, F8, 3) (dual of [8065, 8053, 4]-code or 8065-cap in PG(11,8)), using Gilbert–Varšamov bound and bm = 812 > Vbs−1(k−1) = 1593 047233 [i]
- linear OA(80, 1, F8, 0) (dual of [1, 1, 1]-code), using
- discarding factors / shortening the dual code based on linear OA(80, s, F8, 0) (dual of [s, s, 1]-code) with arbitrarily large s, using
- linear OA(812, 8064, F8, 4) (dual of [8064, 8052, 5]-code), using
- construction X with Varšamov bound [i] based on
- embedding of OOA with Gilbert–Varšamov bound [i] based on linear OA(813, 8066, F8, 4) (dual of [8066, 8053, 5]-code), using
- appending kth column [i] based on linear OOA(813, 8066, F8, 3, 4) (dual of [(8066, 3), 24185, 5]-NRT-code), using
(9, 9+4, 149795)-Net in Base 8 — Upper bound on s
There is no (9, 13, 149796)-net in base 8, because
- the generalized Rao bound for nets shows that 8m ≥ 549757 386739 > 813 [i]