Best Known (168−86, 168, s)-Nets in Base 8
(168−86, 168, 130)-Net over F8 — Constructive and digital
Digital (82, 168, 130)-net over F8, using
- t-expansion [i] based on digital (76, 168, 130)-net over F8, using
- 4 times m-reduction [i] based on digital (76, 172, 130)-net over F8, using
- (u, u+v)-construction [i] based on
- digital (14, 62, 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 (14, 110, 65)-net over F8, using
- net from sequence [i] based on digital (14, 64)-sequence over F8 (see above)
- digital (14, 62, 65)-net over F8, using
- (u, u+v)-construction [i] based on
- 4 times m-reduction [i] based on digital (76, 172, 130)-net over F8, using
(168−86, 168, 225)-Net in Base 8 — Constructive
(82, 168, 225)-net in base 8, using
- base change [i] based on digital (40, 126, 225)-net over F16, using
- net from sequence [i] based on digital (40, 224)-sequence over F16, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F16 with g(F) = 40 and N(F) ≥ 225, using
- net from sequence [i] based on digital (40, 224)-sequence over F16, using
(168−86, 168, 245)-Net over F8 — Digital
Digital (82, 168, 245)-net over F8, using
(168−86, 168, 8114)-Net in Base 8 — Upper bound on s
There is no (82, 168, 8115)-net in base 8, because
- the generalized Rao bound for nets shows that 8m ≥ 52 453055 531710 031209 296316 923456 859424 946270 394191 190762 007318 469914 638806 712237 958411 045253 079425 630577 972802 869728 207595 693934 567185 457809 541246 109696 > 8168 [i]