Best Known (40, 40+18, s)-Nets in Base 9
(40, 40+18, 400)-Net over F9 — Constructive and digital
Digital (40, 58, 400)-net over F9, using
- (u, u+v)-construction [i] based on
- digital (11, 20, 200)-net over F9, using
- trace code for nets [i] based on digital (1, 10, 100)-net over F81, using
- net from sequence [i] based on digital (1, 99)-sequence over F81, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F81 with g(F) = 1 and N(F) ≥ 100, using
- net from sequence [i] based on digital (1, 99)-sequence over F81, using
- trace code for nets [i] based on digital (1, 10, 100)-net over F81, using
- digital (20, 38, 200)-net over F9, using
- trace code for nets [i] based on digital (1, 19, 100)-net over F81, using
- net from sequence [i] based on digital (1, 99)-sequence over F81 (see above)
- trace code for nets [i] based on digital (1, 19, 100)-net over F81, using
- digital (11, 20, 200)-net over F9, using
(40, 40+18, 1625)-Net over F9 — Digital
Digital (40, 58, 1625)-net over F9, using
(40, 40+18, 731511)-Net in Base 9 — Upper bound on s
There is no (40, 58, 731512)-net in base 9, because
- the generalized Rao bound for nets shows that 9m ≥ 22 185403 284783 665890 733083 608681 340477 742980 780359 280065 > 958 [i]