Best Known (13, 18, s)-Nets in Base 8
(13, 18, 4617)-Net over F8 — Constructive and digital
Digital (13, 18, 4617)-net over F8, using
- net defined by OOA [i] based on linear OOA(818, 4617, F8, 6, 5) (dual of [(4617, 6), 27684, 6]-NRT-code), using
- OOA stacking with additional row [i] based on linear OOA(818, 4618, F8, 2, 5) (dual of [(4618, 2), 9218, 6]-NRT-code), using
- (u, u+v)-construction [i] based on
- linear OOA(84, 585, F8, 2, 2) (dual of [(585, 2), 1166, 3]-NRT-code), using
- appending kth column [i] based on linear OA(84, 585, F8, 2) (dual of [585, 581, 3]-code), using
- Hamming code H(4,8) [i]
- appending kth column [i] based on linear OA(84, 585, F8, 2) (dual of [585, 581, 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(84, 585, F8, 2, 2) (dual of [(585, 2), 1166, 3]-NRT-code), using
- (u, u+v)-construction [i] based on
- OOA stacking with additional row [i] based on linear OOA(818, 4618, F8, 2, 5) (dual of [(4618, 2), 9218, 6]-NRT-code), using
(13, 18, 8651)-Net over F8 — Digital
Digital (13, 18, 8651)-net over F8, using
- embedding of OOA with Gilbert–Varšamov bound [i] based on linear OA(818, 8651, F8, 5) (dual of [8651, 8633, 6]-code), using
- (u, u+v)-construction [i] based on
- linear OA(84, 585, F8, 2) (dual of [585, 581, 3]-code), using
- Hamming code H(4,8) [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(84, 585, F8, 2) (dual of [585, 581, 3]-code), using
- (u, u+v)-construction [i] based on
(13, 18, 32640)-Net in Base 8 — Constructive
(13, 18, 32640)-net in base 8, using
- net defined by OOA [i] based on OOA(818, 32640, S8, 5, 5), using
- OOA 2-folding and stacking with additional row [i] based on OA(818, 65281, S8, 5), using
- discarding parts of the base [i] based on linear OA(1613, 65281, F16, 5) (dual of [65281, 65268, 6]-code), using
- OOA 2-folding and stacking with additional row [i] based on OA(818, 65281, S8, 5), using
(13, 18, large)-Net in Base 8 — Upper bound on s
There is no (13, 18, large)-net in base 8, because
- 3 times m-reduction [i] would yield (13, 15, large)-net in base 8, but