Best Known (36−23, 36, s)-Nets in Base 27
(36−23, 36, 96)-Net over F27 — Constructive and digital
Digital (13, 36, 96)-net over F27, using
- t-expansion [i] based on digital (11, 36, 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
(36−23, 36, 136)-Net over F27 — Digital
Digital (13, 36, 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
(36−23, 36, 150)-Net in Base 27 — Constructive
(13, 36, 150)-net in base 27, using
- base change [i] based on digital (4, 27, 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
(36−23, 36, 154)-Net in Base 27
(13, 36, 154)-net in base 27, using
- base change [i] based on digital (4, 27, 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
(36−23, 36, 6761)-Net in Base 27 — Upper bound on s
There is no (13, 36, 6762)-net in base 27, because
- 1 times m-reduction [i] would yield (13, 35, 6762)-net in base 27, but
- the generalized Rao bound for nets shows that 27m ≥ 125 373851 289488 550474 497426 372550 937799 286195 826769 > 2735 [i]