Best Known (40, 40+29, s)-Nets in Base 27
(40, 40+29, 222)-Net over F27 — Constructive and digital
Digital (40, 69, 222)-net over F27, using
- generalized (u, u+v)-construction [i] based on
- digital (4, 13, 64)-net over F27, using
- net from sequence [i] based on digital (4, 63)-sequence over F27, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F27 with g(F) = 4 and N(F) ≥ 64, using
- net from sequence [i] based on digital (4, 63)-sequence over F27, using
- digital (6, 20, 76)-net over F27, using
- net from sequence [i] based on digital (6, 75)-sequence over F27, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F27 with g(F) = 6 and N(F) ≥ 76, using
- net from sequence [i] based on digital (6, 75)-sequence over F27, using
- digital (7, 36, 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 (4, 13, 64)-net over F27, using
(40, 40+29, 370)-Net in Base 27 — Constructive
(40, 69, 370)-net in base 27, using
- 27 times m-reduction [i] based on (40, 96, 370)-net in base 27, using
- base change [i] based on digital (16, 72, 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, 72, 370)-net over F81, using
(40, 40+29, 1477)-Net over F27 — Digital
Digital (40, 69, 1477)-net over F27, using
(40, 40+29, 2083632)-Net in Base 27 — Upper bound on s
There is no (40, 69, 2083633)-net in base 27, because
- 1 times m-reduction [i] would yield (40, 68, 2083633)-net in base 27, but
- the generalized Rao bound for nets shows that 27m ≥ 21 514746 666483 167301 819401 827455 523137 388221 125635 985813 653099 945731 470161 057072 023029 303136 849417 > 2768 [i]