Best Known (40−25, 40, s)-Nets in Base 27
(40−25, 40, 96)-Net over F27 — Constructive and digital
Digital (15, 40, 96)-net over F27, using
- t-expansion [i] based on digital (11, 40, 96)-net over F27, using
- net from sequence [i] based on digital (11, 95)-sequence over F27, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F27 with g(F) = 11 and N(F) ≥ 96, using
- net from sequence [i] based on digital (11, 95)-sequence over F27, using
(40−25, 40, 136)-Net over F27 — Digital
Digital (15, 40, 136)-net over F27, using
- t-expansion [i] based on digital (13, 40, 136)-net over F27, using
- net from sequence [i] based on digital (13, 135)-sequence over F27, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F27 with g(F) = 13 and N(F) ≥ 136, using
- net from sequence [i] based on digital (13, 135)-sequence over F27, using
(40−25, 40, 160)-Net in Base 27 — Constructive
(15, 40, 160)-net in base 27, using
- base change [i] based on digital (5, 30, 160)-net over F81, using
- net from sequence [i] based on digital (5, 159)-sequence over F81, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F81 with g(F) = 5 and N(F) ≥ 160, using
- net from sequence [i] based on digital (5, 159)-sequence over F81, using
(40−25, 40, 167)-Net in Base 27
(15, 40, 167)-net in base 27, using
- base change [i] based on digital (5, 30, 167)-net over F81, using
- net from sequence [i] based on digital (5, 166)-sequence over F81, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F81 with g(F) = 5 and N(F) ≥ 167, using
- net from sequence [i] based on digital (5, 166)-sequence over F81, using
(40−25, 40, 9120)-Net in Base 27 — Upper bound on s
There is no (15, 40, 9121)-net in base 27, because
- 1 times m-reduction [i] would yield (15, 39, 9121)-net in base 27, but
- the generalized Rao bound for nets shows that 27m ≥ 66 566744 607175 259164 367331 197166 659265 031269 289430 388689 > 2739 [i]