Best Known (40−28, 40, s)-Nets in Base 8
(40−28, 40, 48)-Net over F8 — Constructive and digital
Digital (12, 40, 48)-net over F8, using
- t-expansion [i] based on digital (11, 40, 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
(40−28, 40, 49)-Net over F8 — Digital
Digital (12, 40, 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
(40−28, 40, 320)-Net in Base 8 — Upper bound on s
There is no (12, 40, 321)-net in base 8, because
- the generalized Rao bound for nets shows that 8m ≥ 1 379321 004636 850783 857794 754945 460896 > 840 [i]