Best Known (67, 151, s)-Nets in Base 8
(67, 151, 113)-Net over F8 — Constructive and digital
Digital (67, 151, 113)-net over F8, using
- (u, u+v)-construction [i] based on
- digital (11, 53, 48)-net over F8, using
- net from sequence [i] based on digital (11, 47)-sequence over F8, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F8 with g(F) = 11 and N(F) ≥ 48, using
- net from sequence [i] based on digital (11, 47)-sequence over F8, using
- digital (14, 98, 65)-net over F8, using
- net from sequence [i] based on digital (14, 64)-sequence over F8, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F8 with g(F) = 14 and N(F) ≥ 65, using
- the Suzuki function field over F8 [i]
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F8 with g(F) = 14 and N(F) ≥ 65, using
- net from sequence [i] based on digital (14, 64)-sequence over F8, using
- digital (11, 53, 48)-net over F8, using
(67, 151, 160)-Net over F8 — Digital
Digital (67, 151, 160)-net over F8, using
(67, 151, 161)-Net in Base 8
(67, 151, 161)-net in base 8, using
- 1 times m-reduction [i] based on (67, 152, 161)-net in base 8, using
- base change [i] based on digital (29, 114, 161)-net over F16, using
- net from sequence [i] based on digital (29, 160)-sequence over F16, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F16 with g(F) = 29 and N(F) ≥ 161, using
- net from sequence [i] based on digital (29, 160)-sequence over F16, using
- base change [i] based on digital (29, 114, 161)-net over F16, using
(67, 151, 4137)-Net in Base 8 — Upper bound on s
There is no (67, 151, 4138)-net in base 8, because
- the generalized Rao bound for nets shows that 8m ≥ 23326 810034 177162 577423 545213 220438 951279 057257 831892 110650 333991 971713 502405 908128 540933 202399 933972 253158 817354 800133 362493 646804 104816 > 8151 [i]