Best Known (35, 35+40, s)-Nets in Base 27
(35, 35+40, 166)-Net over F27 — Constructive and digital
Digital (35, 75, 166)-net over F27, using
- (u, u+v)-construction [i] based on
- digital (7, 27, 82)-net over F27, using
- net from sequence [i] based on digital (7, 81)-sequence over F27, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F27 with g(F) = 7 and N(F) ≥ 82, using
- net from sequence [i] based on digital (7, 81)-sequence over F27, using
- digital (8, 48, 84)-net over F27, using
- net from sequence [i] based on digital (8, 83)-sequence over F27, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F27 with g(F) = 8 and N(F) ≥ 84, using
- net from sequence [i] based on digital (8, 83)-sequence over F27, using
- digital (7, 27, 82)-net over F27, using
(35, 35+40, 338)-Net over F27 — Digital
Digital (35, 75, 338)-net over F27, using
(35, 35+40, 370)-Net in Base 27 — Constructive
(35, 75, 370)-net in base 27, using
- 1 times m-reduction [i] based on (35, 76, 370)-net in base 27, using
- base change [i] based on digital (16, 57, 370)-net over F81, using
- net from sequence [i] based on digital (16, 369)-sequence over F81, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F81 with g(F) = 16 and N(F) ≥ 370, using
- net from sequence [i] based on digital (16, 369)-sequence over F81, using
- base change [i] based on digital (16, 57, 370)-net over F81, using
(35, 35+40, 74453)-Net in Base 27 — Upper bound on s
There is no (35, 75, 74454)-net in base 27, because
- the generalized Rao bound for nets shows that 27m ≥ 225061 361215 167165 550032 142561 984108 571136 270667 743393 858855 271536 701170 403689 858389 808843 051667 001750 820521 > 2775 [i]