Best Known (48−32, 48, s)-Nets in Base 27
(48−32, 48, 96)-Net over F27 — Constructive and digital
Digital (16, 48, 96)-net over F27, using
- t-expansion [i] based on digital (11, 48, 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
(48−32, 48, 144)-Net over F27 — Digital
Digital (16, 48, 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
(48−32, 48, 150)-Net in Base 27 — Constructive
(16, 48, 150)-net in base 27, using
- base change [i] based on digital (4, 36, 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
(48−32, 48, 154)-Net in Base 27
(16, 48, 154)-net in base 27, using
- base change [i] based on digital (4, 36, 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
(48−32, 48, 5140)-Net in Base 27 — Upper bound on s
There is no (16, 48, 5141)-net in base 27, because
- the generalized Rao bound for nets shows that 27m ≥ 508 946247 100869 898855 987564 740524 662499 292000 404394 459477 558874 725441 > 2748 [i]