Best Known (12, 12+16, s)-Nets in Base 8
(12, 12+16, 48)-Net over F8 — Constructive and digital
Digital (12, 28, 48)-net over F8, using
- t-expansion [i] based on digital (11, 28, 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
(12, 12+16, 49)-Net in Base 8 — Constructive
(12, 28, 49)-net in base 8, using
- base change [i] based on digital (5, 21, 49)-net over F16, using
- net from sequence [i] based on digital (5, 48)-sequence over F16, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F16 with g(F) = 5 and N(F) ≥ 49, using
- net from sequence [i] based on digital (5, 48)-sequence over F16, using
(12, 12+16, 49)-Net over F8 — Digital
Digital (12, 28, 49)-net over F8, using
- net from sequence [i] based on digital (12, 48)-sequence over F8, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F8 with g(F) = 12 and N(F) ≥ 49, using
(12, 12+16, 774)-Net in Base 8 — Upper bound on s
There is no (12, 28, 775)-net in base 8, because
- the generalized Rao bound for nets shows that 8m ≥ 19 515890 953135 497682 608736 > 828 [i]