Best Known (168−34, 168, s)-Nets in Base 8
(168−34, 168, 1955)-Net over F8 — Constructive and digital
Digital (134, 168, 1955)-net over F8, using
- (u, u+v)-construction [i] based on
- digital (5, 22, 28)-net over F8, using
- net from sequence [i] based on digital (5, 27)-sequence over F8, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F8 with g(F) = 5 and N(F) ≥ 28, using
- net from sequence [i] based on digital (5, 27)-sequence over F8, using
- digital (112, 146, 1927)-net over F8, using
- net defined by OOA [i] based on linear OOA(8146, 1927, F8, 34, 34) (dual of [(1927, 34), 65372, 35]-NRT-code), using
- OA 17-folding and stacking [i] based on linear OA(8146, 32759, F8, 34) (dual of [32759, 32613, 35]-code), using
- discarding factors / shortening the dual code based on linear OA(8146, 32768, F8, 34) (dual of [32768, 32622, 35]-code), using
- an extension Ce(33) of the primitive narrow-sense BCH-code C(I) with length 32767 = 85−1, defining interval I = [1,33], and designed minimum distance d ≥ |I|+1 = 34 [i]
- discarding factors / shortening the dual code based on linear OA(8146, 32768, F8, 34) (dual of [32768, 32622, 35]-code), using
- OA 17-folding and stacking [i] based on linear OA(8146, 32759, F8, 34) (dual of [32759, 32613, 35]-code), using
- net defined by OOA [i] based on linear OOA(8146, 1927, F8, 34, 34) (dual of [(1927, 34), 65372, 35]-NRT-code), using
- digital (5, 22, 28)-net over F8, using
(168−34, 168, 3855)-Net in Base 8 — Constructive
(134, 168, 3855)-net in base 8, using
- base change [i] based on digital (92, 126, 3855)-net over F16, using
- 161 times duplication [i] based on digital (91, 125, 3855)-net over F16, using
- net defined by OOA [i] based on linear OOA(16125, 3855, F16, 34, 34) (dual of [(3855, 34), 130945, 35]-NRT-code), using
- OA 17-folding and stacking [i] based on linear OA(16125, 65535, F16, 34) (dual of [65535, 65410, 35]-code), using
- discarding factors / shortening the dual code based on linear OA(16125, 65536, F16, 34) (dual of [65536, 65411, 35]-code), using
- an extension Ce(33) of the primitive narrow-sense BCH-code C(I) with length 65535 = 164−1, defining interval I = [1,33], and designed minimum distance d ≥ |I|+1 = 34 [i]
- discarding factors / shortening the dual code based on linear OA(16125, 65536, F16, 34) (dual of [65536, 65411, 35]-code), using
- OA 17-folding and stacking [i] based on linear OA(16125, 65535, F16, 34) (dual of [65535, 65410, 35]-code), using
- net defined by OOA [i] based on linear OOA(16125, 3855, F16, 34, 34) (dual of [(3855, 34), 130945, 35]-NRT-code), using
- 161 times duplication [i] based on digital (91, 125, 3855)-net over F16, using
(168−34, 168, 74456)-Net over F8 — Digital
Digital (134, 168, 74456)-net over F8, using
(168−34, 168, large)-Net in Base 8 — Upper bound on s
There is no (134, 168, large)-net in base 8, because
- 32 times m-reduction [i] would yield (134, 136, large)-net in base 8, but