Best Known (28−17, 28, s)-Nets in Base 27
(28−17, 28, 96)-Net over F27 — Constructive and digital
Digital (11, 28, 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
(28−17, 28, 100)-Net over F27 — Digital
Digital (11, 28, 100)-net over F27, using
- net from sequence [i] based on digital (11, 99)-sequence over F27, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F27 with g(F) = 11 and N(F) ≥ 100, using
(28−17, 28, 150)-Net in Base 27 — Constructive
(11, 28, 150)-net in base 27, using
- base change [i] based on digital (4, 21, 150)-net over F81, using
- net from sequence [i] based on digital (4, 149)-sequence over F81, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F81 with g(F) = 4 and N(F) ≥ 150, using
- net from sequence [i] based on digital (4, 149)-sequence over F81, using
(28−17, 28, 154)-Net in Base 27
(11, 28, 154)-net in base 27, using
- base change [i] based on digital (4, 21, 154)-net over F81, using
- net from sequence [i] based on digital (4, 153)-sequence over F81, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F81 with g(F) = 4 and N(F) ≥ 154, using
- net from sequence [i] based on digital (4, 153)-sequence over F81, using
(28−17, 28, 9803)-Net in Base 27 — Upper bound on s
There is no (11, 28, 9804)-net in base 27, because
- 1 times m-reduction [i] would yield (11, 27, 9804)-net in base 27, but
- the generalized Rao bound for nets shows that 27m ≥ 443 446936 908923 763789 506629 004376 728001 > 2727 [i]