Best Known (13, 13+21, s)-Nets in Base 27
(13, 13+21, 96)-Net over F27 — Constructive and digital
Digital (13, 34, 96)-net over F27, using
- t-expansion [i] based on digital (11, 34, 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
(13, 13+21, 136)-Net over F27 — Digital
Digital (13, 34, 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
(13, 13+21, 150)-Net in Base 27 — Constructive
(13, 34, 150)-net in base 27, using
- 2 times m-reduction [i] based on (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
- base change [i] based on digital (4, 27, 150)-net over F81, using
(13, 13+21, 154)-Net in Base 27
(13, 34, 154)-net in base 27, using
- 2 times m-reduction [i] based on (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
- base change [i] based on digital (4, 27, 154)-net over F81, using
(13, 13+21, 9210)-Net in Base 27 — Upper bound on s
There is no (13, 34, 9211)-net in base 27, because
- 1 times m-reduction [i] would yield (13, 33, 9211)-net in base 27, but
- the generalized Rao bound for nets shows that 27m ≥ 171925 553293 463383 565208 178085 428656 062258 146773 > 2733 [i]