Best Known (40−24, 40, s)-Nets in Base 27
(40−24, 40, 96)-Net over F27 — Constructive and digital
Digital (16, 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
(40−24, 40, 144)-Net over F27 — Digital
Digital (16, 40, 144)-net over F27, using
- net from sequence [i] based on digital (16, 143)-sequence over F27, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F27 with g(F) = 16 and N(F) ≥ 144, using
(40−24, 40, 160)-Net in Base 27 — Constructive
(16, 40, 160)-net in base 27, using
- 4 times m-reduction [i] based on (16, 44, 160)-net in base 27, using
- base change [i] based on digital (5, 33, 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
- base change [i] based on digital (5, 33, 160)-net over F81, using
(40−24, 40, 190)-Net in Base 27
(16, 40, 190)-net in base 27, using
- base change [i] based on digital (6, 30, 190)-net over F81, using
- net from sequence [i] based on digital (6, 189)-sequence over F81, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F81 with g(F) = 6 and N(F) ≥ 190, using
- net from sequence [i] based on digital (6, 189)-sequence over F81, using
(40−24, 40, 12005)-Net in Base 27 — Upper bound on s
There is no (16, 40, 12006)-net in base 27, because
- the generalized Rao bound for nets shows that 27m ≥ 1797 670520 147046 262336 794877 420260 650473 254667 782723 625817 > 2740 [i]